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1 














GRAND STAIRCASE, AND SPACIOUS ELEGANTLY FITTED H -Frontispiece. 






















































































































































































































































































































































































STAIR-BUILDING 


IK ITS VARIOUS FORMS; 


AND 


The New One-Plane Method 


OF 


HAND-RAILING 


AS APPLIED TO 

Drawing Face-Moulds, 

Unfolding the Centre Line of Wreaths, 

AND 

GIVING LENGTHS OF BALUSTERS 

UNDER ALL WREATHS. 



OF STUBS, lEWElS IMD BIIHSTEHS 


FOR THE USE OF 

ARCHITECTS, 



By JAMES H. MONCKTON, 

» 

Author of the American Stair-Builder ” Monckton s National Carpenter and Jomerf ^^Monckton's Stair- 
Builder,” and “ Monckton’s Practical Geoitietry”; Teacher for many years of the Mechanical 
Class in the “ General Society of Mechanics and Tradesmen's Free 
Drawing School of the City of New York,” 



NEW YORK: 

JOHN WILEY & SONS, 

15 Astor Place. 


1888. 










Copyright, i 8 S 3 . 

By JAMES H. MONCKTON. 




DnuxMo^n) & Ncu 
Elrctrot’ipers, 



PREFACE. 


This book presents for the first time—as applied to hand-railing —the one-plaiie method of draw¬ 
ing face-moulds, a method in which only one plane of projection is required; the simplicity, rapidity 
and convenience of which in practice make it superior to all others. By the one-plane process of 
drawing a face-mould, a centre line of wreath may also be unfolded and fixed in its relation to the 
elevation of tread and rise; thus determining the length of each baluster on the curved plan and gain¬ 
ing a knowledge and control of the wreath’s exact position not before attainable. 

It is intended to make this book a complete work on stair-building and hand-railing, giving a 
large selection of plans and designs of staircases, newels and balusters, and numerous examples of 
construction. The paper solids here introduced as an objective means of elementary and practical 
instruction in the principles and geometrical methods of hand-railing are unequalled for the pur¬ 
pose, as the construction of these solids with the drawings on their surfaces show all the positions 
and connections required in each case, and thereby enable any fairly intelligent person to understand 
and grasp the subject. The professional architect will find valuable suggestions in design and 
construction ; also important considerations in planning stairs. 

The experienced stair-builder will learn that this one-plane method of drawing all face-moulds— 
and also the manner of finding the angles with which to square wreath-pieces—is simple, uniform and 
rapid ; and no matter how skilful a stair-builder he may be, he will find that, in the extent and com¬ 
pleteness of detail with which the subject is treated, it will prove a valuable work of reference. The 
expert rail-worker will learn of the geometrical law controlling the top and bottom curves of every 
wreath-piece, showing that a face-mould is not only a means of shaping the sides of a wreath-piece on 
the plane of the plank, but that it carries with it a central geometrical curve (a helical line) that must 
be observed in shaping the top and bottom surfaces of the wreath. To prove this in a practical way 
it is only necessary to call attention to the fact that in the case of round hand-rail over any curved 
plan, its sides hang vertically over the plan, while its top and bottom form proper curves giving its 
own casings perfectly suited to the requirements in all cases ; and when it is considered that a 
moulded rail over the same plan would be subject to ihe same centre and tangents, with the same 
joints, then the absolute control of the curves forming the top and the bottom of a wreath by this 
central geometrical curve line becomes self-evident. In connection with the above statements examine 
for instance Plate 48, as giving one example among many of the correctness and practical value of un¬ 
folding the centre line of a wreath. 

The student or apprentice will find that the elementary study of hand-railing in the practical and 
novel way here presented is easily acquired ; he will also see that the detail instruction given in stair¬ 
building from a stepladder to expensive and difficult staircases is presented in a manner to be clearly 
understood and quickly learned. That the drawings and descriptive page should be opposite I regard 
as of no slight importance in a work of this character ; those who have experienced the weary task of 
turning trom reference pages to plates located at another portion of the book will appreciate the value 
of this arrangement. The comprehensive system of hand-railing here given covers every practical re¬ 
quirement, as follows: ist. By the use of tangents controlling the inclination of the plane of the plank 
and the butt joints ; 2d. By the one-plane method of drawing all face-moulds, simply applying to this 
purpose a level line common to both planes ; 3d. By the further use of this last-mentioned level line, in 
unfoldl-ng the centre line of wreath;—all of which are based upon the demonstrable laws of geometry, 
and point to a conclusion in the science of hand-railing as plain as that in the decimal system of num¬ 
bers, which, based upon the ever-truthful laws of that branch of mathematics, is simple in its methods 
and perfect in its results. 

Finally, it is my belief that this work is carried to an extent far beyond any publication that has 
preceded it; practically and scientifically covering the whole field of stair-building and hand-railing, 
making a complete digest of the subject. 

The interesting interiors on Frontispiece and Plates 68 and 69 were kindly furnished to the 
author by the well-known architect Mr. W. H. Hume, 2 West Fourteenth Street, New York City. 
The reader will find that, in addition to being an embellishment to this work, their careful exami¬ 
nation will well repay his study. 

Jas. H. Monckton. 



4 


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CONTENTS. 


PLANS AND ELEVATIONS. 


PLATE 1 . 

Plan and elevation of a straight flight of stairs with a 7" cylinder. Plan and elevation of a half-turn 
platform stairs with a 6" cylinder, landing with four rises above the platform. A rule io find the correct 
proportion of tread to rise. 

PLATE 2 . 


STEP-LADDERS AND STOOP. 

Plans of step-ladders. Elevations of step-ladders. Elevation of stoop with platform, hand-rail, balusters 
and newel. 


PLATE 3 . 

The old Eni^lish method of stair-buildinq-. Finishing stairs on the under-side, showing the construction. 
Ptdtinq up stairs. Covering stairs. Stair-timbering and rongh-brachetiiig. Best method of joining hand¬ 
rail to newel. Plan and elevation of a common straight flight of stairs. Metliods of making ordinary 
small cylinders and splicing them to strings. Front and wall strings laid out. Step and riser as worked 
and glued together. 

PLATE 4 . 

PLANNING WINDING STAIRS. 

Line of travel fixed. Elevation of the winding flight given. Laying out the front-string and cylinders. 
Laying out the wall-strings. 

PLATE 5 . 

PLANNING STAIRS. 

In the following three Plates—5, 6 and 7—over thirtv different plans of stairs are given; their various 
dimensions are figured for the convenience of examination and use in the study and planning of stairs. 
Also reference is given to each Plate, where a drawing of the plan of stairs is again projected on a large 
scale, together with the managetnent of the hand-rail wreath. 

Fig. 1 . Plan of a straiglit flight of stairs starting and landing with small cylinders. See Plate i. 
Figs, i and 2: also Plates 3 and 22. 

Fig. 2 . Plan of a straight flight of stairs starting with a newel set off 2^', and landing with a 7" 
cylinder, the landing riser set into the cylinder 2\". See Plate 30, Figs i and 2: also Plates 33 and 34. 

Fig. 3 . Plan of winding stairs suitable for Basement or Attic Story, with mortised—or housed—strings 
both sides; intended to be set between partitions or otherwise enclosed. 

Fig. 4 . Shows the manner of laying out the front string. A and B are continuations of the string, 5" 
wide, and spliced to the string as shown. 

Fig. 5 . Plan of a quarter-turn of winders, with cylinder, suitable for either the starting or landing of a 
flight of stairs. See Plate 25. 

Fig. 6. A much superior plan to that of Fig. 5, turning one quarter without winders, and with the same 
size of cylinder and regular tread. In this plan, by curving the front ends of two risers, winders are dispensed 
with and a platform and parallel steps substituted ; this plan as shown at D C requiring ’]\" more run. See 
Plate 26. 

Fig. 7 . Plan the same as Fig. 6, but instead of a continued hand rail a small newel and connecting level 
quarter-cylinder are substituted. See Plate 62. 

Fig. 8. Plan for starting or landing a flight of stairs, with a single newel set diagonally. 

Fig. 9 . Plan of stairs combining two platforms with a parallel step between (and the front ends of its 
two risers curved), making a half turn. See Plate 41. 

Fig. 10 . Plan of a quarter-platform stairs, showing how to place the risers connecting with any quarter- 
cylinder so that the wreath may be worked in one piece on a common inclination and in the best possible 
shape. On these plans, from the face of the riser F and on the centre line of the rail, F E should equal half 
a tread; and from the face of the riser G on the centre line of rail, G E must equal half a tread. See Plate 
31, Fig. 3. and Plate 37, Fig.s. 5, 6 and 7. 

Fig. 11 . Plan of stairs, with a quarter-cylinder turning one quarter, with winders. See Plate 36. 

PLATE 6. 

PLANNING STAIRS. 

Fig. 1 . Plan of half turn platform stairs with the risers set in the cylinder as far as possible to save run. 
The cylinder-opening is made up of two 6" quarter-circles and 5" straight between. See Plate 38. 



Vlll 


CONTENTS. 


Fig. 2 . Plan of a flight of winding stairs with lo" cylinders, making a half-turn at the starting and at the 

landing. See Plates 28 and 29. « 1 ■ 

Fig. 3 . Plan of two connecting flights starting and landing from one 12" cylinder; the flight starting 
turning one quarter with winders, the other flight straight and landing straight, with its top riser set into 
the cylinder 4". See Plate 42. 

Fig. 4 . Plan of a landing or starting of a flight of stairs, with a single newel set between quarter-cylinders. 

See Plate 37, Figs. i. 2, 3 and 4. . . , , 

Fig. 5 . Plan of the starting of a flight of stairs, with the front-string curved out. including four treacs 
Each of tlie four treads are increased in width at the wall-string and diminished at the front-string, 
curving the risers,—making what are called swell steps. See Plate 32. 

Fig. 6. Plan of the starting or landing of a flight, turning one quarter, with platform; finished with low- 
down newels, or—more properly—small corner-pieces, and continued liand-rail with ramp and goose-neck. See 
Plate 58, 

Fig. 7 . Plan of half-turn platform open-newel stairs with wing-flights. 

Fig. 8. Plan of half-turn platform stai'rs with a large cylinder into which the front ends of the risers of 
parallel steps are brought curved; thus utilizing the cylinder-space and making a half-turn without resorting 
to winders. See Plate 51. 

Fig. 9 . Plan of ship or steamboat stairs. At Plate 52 is a plan similar to this with angle newels. See 
also Plate 50. 


PLATE 7 . 

PLANNING STAIRS. 

Fig. 1 . Plan of half-turn platform-stairs with a 15" cylinder; the risers at the platform and at the starting 
cf the flight are set in the cylinders 6", thereby saving I'.o" of run. See PLATE 40. 

Fig. 2 . Plan of a half-turn platform stairs with a central riser making two platforms, and the starting 

and landing risers each set into the cylinder 3". .See Plate 39. 

Fig. 3 . Plan of a flight of stairs winding one quarter at the starting and one half at about the middle 

of the flight. For the treatment of the hand-rail at the starting see Plate 48, and for the treatment of the 

rail at the half-turn see Plate 47. 

Fig. 4 . Plan of the bottom or top portion of a flight of stairs making a quarter-turn with a quarter- 
platforni, the plat/'orm and parallel steps secured and 'winders avoided, by curving the front ends of risers 
to the widths of treads marked on the line of cylinder. The cylinder opening is formed of two quarter- 
circles. each of 5" radius with 8'' straight between. For treatment of hand-rail with larger scale-drawing 
see Plate 46. 

Fig. 5 . Plan of the bottom or top portion of a flight of open-newel stairs with a 15" opening, making 
a quarter turn w'ith a quarter-platform. See Plate 59. 

Fig. 6. Plan of the bottom or top portion of a flight of stairs with a 10" cylinder winding one 

quarter. For treatment of wreath at the bottom of a flight see Plate 27, and for the top of a flight 
the same as at Plate 25. 

Fig. 7 . Plan similar to FiG. 6, with one more winder in the plan and curved risers introduced to 
save room between the points B and C. 

Fig. 8. Plan same as' FiG. 4, with a complete semicircle for cylinder opening. For treatment of 

wreath see Pl.ate 44. 

Fig. 9 . Plan of the top or bottom portion of a flight of stairs making a quarter turn with a quarter- 
platform and a parallel step set at the centre of a 15" cylinder. See Plate 43 for larger size scale¬ 
drawing and management of wreath. 

Fig. 10 . Plan of a flight of circular stairs. The dotted lines show the best method of placing the 
carriage-timbers. The treatment of hand-rail on a larger scale of drawing will be found at Plate 53. 
At Pl.ate 54 fidl instruction is given for changing the plan of the first step to the scroll form ; the treat¬ 
ment of that portion of the hand-rail, also the construction of the scroll-step. 

Fig. 11 . Plan of an elliptic flight of stairs with the treads at the wall and front-strings properly 
graded so as to bring the risers on lines more nearly normal to the curves and at the same lime main¬ 
tain an even tread on the line of travel. These stairs should be timbered in the manner shown at FiG. 10. 

Self-supporting stairs, also see Plate 45. 


PLATE 8. 

Figs. 1 and 2 . Bending wood by saw-kerfing and the construction of a circular form, with ribs of the 
proper curve an;l narrow strips of the required length called laggings, over which to bend the saw-kerfed material. 

Fig. 3 . Bending wood on a curved form and keying. 

Fig. 4 . Bending veneer, facing and filling out the thickness with parallel pieces—fitted to the curve— 
called staves. 

Fig. 5 . Laminated work—bending and gluing several thickness of veneer together. A rule to ascertain 
•what thickness of 'white pine will bear bending any given radius of ctirvature without injttrin^ its elasticity. 

Fig. 6. Bend ing stair-strings. 

Figs. 7 and 8. Construction of a form for bending quarter-circle stair-strings, the ribs to stand on an 
angle parallel to the inclination of string. 

Figs. 9 and 10 . Soffit-mouldings on the lower edge of cylinders. 

Figs. 11 and 12 . To find the lengths of cylinder-staves that include winder-treads. 


PLATE 9 . 

Examples of the one-plane method in drawing face-moulds. 


Face-moulds, their number and character. 






CONTENTS. 


IX 


ELEMENTARY INSTRUCTION IN HAND-RAILING OVER 

CURVED PLANS. 

PLATE 10. 

Face-mould and parallel pattern over a plan of a quarter-circle; one tangent inclined, the other horizontal. 
The angles with which to square the wreath-piece at the joints. 

PLATE 11. 

Face-mould and parallel pattern over a plan of a quarter-circle, the tangents inclined alike. The angle 
with which to square the wreath-piece at both joints. 

PLATE 12. 

Face-mould and parallel pattern over a plan of a quarter-circle, the tangents differently inclined. The 
angles with which to square the wreath-piece at the joints. 

PLATE 13. 

Face-mould and parallel pattern over a plan less than a quarter-circle, one tangent inclined, the other 
horizontal. The angles with which to square the wreath-piece at the joints. 

PLATE 14. 

Face-mould and parallel pattern over a plan of more than a quarter-circle, one tangent inclined, the other 
horizontal. The angles with which to square the wreath-piece at the joints. 

PLATE 15. 

Face-mould over a plan less than a quarter-circle, the tangents inclined alike. The angle with which to 
square the wreath-piece at both joints. 


PLATE 16. 

Face-mould over a plan less than a quarter-circle, the tangents differently inclined. The angles with 
w'hich to square the wreath-piece at the joints. 


PLATE 17. 

Face-mould over an elliptic or eccentric curved plan, the tangents of unequal length and different inclina¬ 
tions. The angles with which to square the wreath-piece at the joints. To find a common angle of inclina¬ 
tion over two different lengths of plan tangents—ivhen required—the total height being given. 

PLATE 18. 

Face mould or parallel pattern over a plan greater than a quarter-circle, the tangents inclined alike. The 
angle with which to square the wreath-piece at both joints. 

PLATE 19. 

Face-mould over a plan greater than a quarter-circle, the tangents differently inclined. The angles with 
which to square the wreath-piece at the joints. 


DEVELOPMENT OR UNFOLDING OF THE CENTRE LINE OF 

WREATHS. 

PLATE 20. 

Fig. 1 . Plan of a centre line of wreath, a semicircle with three tangents inclined alike, the fourth tangent 
level. 

Fig. 2 . The centre line of wreath unfolded from plan Fig. i. 

Fig. 3 . Plan of a centre line of wreath, a semicircle with two tangents inclined alike, the third of a less 
inclination, and the fourth tangent level. 

Fig. 4 . The centre line of wreath unfolded from plan Fig. 3. 

Fig. 5 . Plan of a centre line of wreath-piece less than a quarter-circle, one tangent inclined, the other 
level. 

Fig. 6. The centre line of wreath-piece unfolded from plan Fig. 5. 



X 


CONTENTS. 


PLATE 21. 

Fig. 1. Plan of a centre line of wreath-piece greater than a quarter-circle, one tangent inclined, the other 
level. 

Fig. 2. The centre line of wreath-piece unfolded from plan Fig. i. / -i 

Fig. 3. Plan of a centre line of wreath-piece greater than a quarter-circle, the tangents of a like 

inclination. 

Fig. 4. The centre line of wreath-piece unfolded from plan Fig. 3. 

Fig. 5. Plan of a centre line of wreath-piece greater than a quarter-circle, the tangents differently 

inclined. 

Fig. 6. The centre line of wreath-piece unfolded from plan Fig. 5. 

Fig. 7. Plan of a centre line of wreath-piece less than a quarter-circle, the tangents inclined alike. 

Fig. 8. The centre line of wreath-piece unfolded from plan Fig. 7. 

Fig. 9. Plan of a centre line of wreath-piece less than a quarter-circle, the tangents inclined differently. 

Fig. 10. The centre line of wreath-piece unfolded from plan Fig. 9 . 

PLATE 22. 

POSITION OF RISERS IN CONNECTION WITH CYLINDERS AT THE STARTING AND AT THE 

LANDING OF STRAIGHT FLIGHTS OF STAIRS. 

Fig. 1. Elevation of rises and tread to determine the face of riser at the bottom of a flight when the 
over-wood is to be all removed from the top of the wreath-piece. 

Fig. 2. Elevation of tread and rise at the top of a flight to determine— when all the over-7uood is removed 
from the bottom of a wreath-piece —the relative position of the riser and cylinder. 

Fig. 3 . Plan of the bottom of flight with riser and cylinder placed as determined at FiG. i. 

Fig. 4. Plan of the top of flight with cylinder and riser as determined by trial at FiG. 2. 

Fig. 5. Face-mould. 

Fig. 6. Perspective sketch of the wreath-piece, showing both joints prepared for squaring and the applica¬ 
tion of the face-mould both sides of the plank. 

Fig. 7. Elevation of tread and rises for the top and bottom of flight, showing that in some cases by a 
change in removing the over-wood the risers may be placed at the chord-lines of cylinders of this diameter. 

PLATE 23. 

Half-turn Platform Stairs as given by plan and elevation at Plate i. Figs. 3 and 4. How to fix 
the position of risers in connection with the cylinders, and the changes possible by varying the removal of 
over-wood from the straight portion of wreath-pieces, see ,FlGS. i and 2 ; also how to place the risers 

connecting with the cylinder of a half-turn platform stairs so that the wreath may have a common incli¬ 

nation, making a much superior-shaped rail and saving several inches more room than by the method 
given at Fig. 2. See Figs. 3, 4 and 5. 


PLATE 24. 

Fixing the position of risers connecting with 15" cylinders at the starting and at the landing of 
straight flights of stairs, so that the over-wood may be removed in the most desirable way to shape the 
wreath-pieces, and raise the height required from the floor.—FiGS. i, 2 and 3. 

Plan of stairs with the top riser placed at the diameter-line of a 15" cylinder; management of hand¬ 
rail, etc.—F igs. 4, 5 and 6. 


PLATE 25. 

Fig. 1. Plan of the top portion of a staircase winding one quarter, with a small cylinder. 

Fig. 2. Elevation of treads and rises; development or unfolding of the centre line of wreath. Plans 

of hand-rail and face-moulds. Figs. 3 , 4 , 5 and 6 . 


PLATE 26. 

Fig. 1. Improved plan of the top portion of a staircase winding one quarter, with a small cylinder. 
Fig. 2. Elevation of treads and rises; development of the centre line of wreath; length of balusters. 
Plans of hand-rail and face-moulds. Figs. 3, 4, 5 and 6. 


PLATE 27. 

Fig. 1. Plan of the bottom portion of a staircase winding one quarter, with a 10 '' cylinder. 

Fig. 2. Elevation of treads and rises from plan FiG. i ; also development of the centre line of wreath 

giving lengths of balusters under wreath. Plans of hand-rail and face-moulds. Figs. 3. 4, 5 and 6. 

PLATE 28. 

Fig. 1. Plan of the top portion of a winding staircase, making a half-turn, with a 10 " cylinder. 

Fig. 2. Elevation of treads and rises and development of the centre line of wreath, giving lengths 01 

b&lustcrs, etc. 

Figs. 3 and 4 . Plan of hand-rail and face-mould. Fig. 4. Face-mould for both quarters of the cylinder 
the easement at the top finishing to a level from the upper end of wreath. 


CONTENTS. 


xi 


PLATE 29. 

Plan of the bottom portion of a winding staircase making a half-turn, with a lo" cylinder. 

Fig. 1. Elevation of treads and rises as given at plan FiG. i ; also unfolding the centre line of wreath, 
giving lengths of balusters, etc. 

If'ig. 2. Plan of hand-rail and face-mould. 

Figs. 3 and 4. Face-mould for both quarters. 


PLATES 30, 31, 32. 

At the starting of a first flight of stairs the front-string is frequently curved out, the curve extending 
from one to five treads. 

Management of Strings and Hand-rails of Curve-outs. 

Plate 30.— Fig. i. Plan and elevation. Fig. 2 . Parallel pattern. Fig. 3 . Plan and elevation of the starting 
of a staircase, with the front-string curved out and the newel set on top of the first step. Fig. 4 . Parallel 
pattern for curve-out of hand-rail, easing to a level at newel. 

Plate 31.— Fig. i. Plan and elevation of the starting of a staircase, with the front-string curved out and 
the newel set on top of the first step. This plan is the same as that of Fig. 3, Plate 30, but in this 
case the hand-rail is brought straight down to the newel, not easing to a level as at Plate 30. FiG. 2. 
Face-mould for FiG. i. FiG. 3. Plan of a quarter-platform stairs with a quarter-cylinder of 8" radius, the 
risers improperly set at the chord-lines, thereby making it necessary to get out the quarter-wreath in two 
pieces. Fig. 4 . Parallel pattern, two of which make the quarter-wreath. 

Plate 32.— Fig. i. Plan of curve-out,—with four steps,—its shape designed to make a proper connection 
with a square newel, where the sides of the newel are required to set parallel to the side-walls of the hall- 
Avay. Fig. 2. Elevation of treads and rises from plan Fig. i. Fig. 3. Face-mould from Fig. i. showing 
the squaring of the wreath-piece at the joints. Fig. 4. Plan of starting a staircase, with the front-string 
curved out, embracing four treads of equal widths at the wall-string and front-string. FiG. 5. Elevation 
‘of treads and rises from plan FiG. 4 . FiG. 6 . Face-mould from plan FiG. 4 , showing the squaring of 
wreath-piece at the joints. 

PLATE 33. 

Fig. 1. Plan of the landing of a straight flight of stairs, with the top riser set in the whole depth 
of a ten-inch cylinder, thereby savins^ five inches. 

Fig. 2. Elevation of tread and rises from plan Fig. i. 

Fig. 3. Face-mould from plan Fig. i ; also showing the squaring of the wreath-piece at the joints. 

Fig. 4. Plan of the starting portion of the same flight of stairs given at FiG. i. with a ten-inch 

cylinder, and the starting riser set in the whole radius, or depth, of cylinder, saving another five inches. 

Fig. 5 . Elevation of tread and rises from plan Fig. 4. 

Fig. 6. Elevation of tread and rises same as Fig. 5, showing the unfolding of the centre line of wreath. 


PLATE 34. 

Hand-rail wreath in one piece over a 7 " cylinder, the landing riser set in the radius— 3 T'— 

OF THE CYLINDER. 

PLATE 35. 

Hand-rail wreath in one piece over a 7" cylinder by a different method from that given 
AT Plate 34. In this case the landing riser is placed at the chord-line of the cylinder. Figs. 
4 and 5 . Wainscoting for stairs, its heights and construction. 


PLATE 36. 

Plan of winding stairs turning one quarter, with a quarter-cylinder of 8 " radius. Elevation from plan. 
Unfolding' the centre line of wreath. Length of balusters under wreath. Parallel pattern for wreath-piece. 
See Plate 5 , Fig. ii. 


PLATE 37. 

Plan of half-turn platform stairs. Where to place the risers connecting with the cylinder when the 
over-wood is to be removed from the wreath-pieces as shown. Drawing the face-mould for the quarter- 
cylinders. Plan of quarter-turn platform stairs, with a quarter-cylinder of 6 " radius. Where to place the 
risers connecting with the quarter-cylinder. Elevation of plan, and unfolding the centre line of wreath. 
Drawing the face-mould. See Plate 5. Fig. 10 ; also Plate 45, Fig. i. 


PLATE 38. 

Plan of half-turn platform stairs, with the risers next to platform set in the whole depth of the cyl¬ 
inder. Elevation from plan and unfolding the centre line of wreath. Lengths of balusters under wreath. 
Drawing the face-mould. 


CONTENTS. 


xii 


PLATE 39. 

Plan of half-turn platform stairs, with one riser set at the centre of the cylinder dividing the half¬ 
turn space in two platforms ; the other two connecting risers each set in the cylinder . Elevation fiom 
plan. Unfolding the centre line of wreath. Drawing the face-mould. 

PLATE 40. 

Plan of half-turn platform stairs, with two risers each set into the 15 " cylinder 6 ". The bottom riser 
set into the cylinder at the starting of the flight as found on trial from elevation. Drawing face-moulds. 
See Fig. i, Plate 7 . 


PLATE 41. 

Plan of stairs with two quarter platforms and a tread between, making a half-turn. Elevation from 
plan. Unfolding the centre line of wreath. Drawing the face-mould. 

PLATE 42. 

Plan of stairs in which two flights start and land in connection with a 12 " cylinder, the upper flight 
starting and turning one quarter with winders, the lower flight straight with the landing riser set 4 " into 
the cylinder. Elevation from plan and unfolding the centre line of wreath. Drawing the face-moulds. 
See Plate 6, Fig. 3. 


PLATE 43. 

Plan of stairs making a quarter-turn, with a 15 " cylinder, a quarter platform, and a parallel step set 
in the centre of the cylinder and at right angles to its diameter. Elevation from plan and unfolding the 
centre line of wreath. Drawing the face-moulds. Showing that in some cases greater width of wood than 
the width of face-mould is required for the wreath. See Plate 7, Fig. 9. 


PLATE 44. 

Plan of stairs turning one quarter, with an 18 '' cylinder, a quarter-platform, and three steps with 
their front ends curved to the cylinder, designed to take the place of winders. Elevation from plan and 
unfolding the centre line of the wreath, by means of which the lengths of balusters under the wreath may 
be found. Drawing the face-moulds. See Plate 7, Fig. 8. 


PLATE 45. 

Plan of circular stairs winding around a circular post. Plan of stairs with close string, showing how 
to build the cylinder solid with veneered faces. Plan of quarter-platform stairs, showing how to place the 
risers in the quarter-cylinder another way (when desirable), different from the one given at Plate 37, 
Fig. 5 , and Plate 5, Fig. 10. 


PLATE 46. 

Plan, turning one quarter, with a quarter-platform, designed to avoid winders by curving the front 
ends of the parallel steps to the cylinder. Elevation from plan and unfolding the centre line of wreath, 
by means of which the lengths of balusters under the wreath may be found. Drawing the face-moulds. 
See Plate 7, Fig. 4. 


PLATE 47. 

Plan of half-turn winding stairs with 7 " cylinder. Elevation from plan, and unfolding the centre line of 
w'reath, by means of which the lengths of balusters under the wreath may be found. Drawing the face-mould 
See Plate 6 , Fig. 2 . 


PLATE 48. 

Plan of a starting portion of a flight winding one quarter from a newel, the hand-rail wreath coverin" 
nearly a semicircle on the plan, worked in one piece and no ramp used in connection. Elevation from plan 
and unf(ffding the centre line of wreath, by means of which the length of each baluster under the wreath is 
given. Drawing a parallel pattern for the wreath-piece. 


PLATE 49. 


Plan of the starting portion of a flight winding more than a quarter from a newel, with a 20 " cylinder 
containing five winders. The wreath covering nearly a semicircle on the plan, worked in one piece and 
'u Elevation from plan and unfolding the centre line of wreath, by means of 

which the length of each baluster under the wreath is given. Sketch, showing the wreath as squared 
up. Drawing the face-mould. See Plate 7 , Fig. 3 . » 4 


CONTENTS. 


Xlll 


PLATE 50. 

Plan for hand-rail with parallel patterns for wreath-pieces, the plan taken trom Plate 6, Fig. 9. 
Steamship stairs. Elevation from plan and unfolding the centre line of wreath, showing the length of 
each baluster under the wreath. 


PLATE 51. 

Plan of half-turn platform stairs with six parallel steps, and platform placed in a large cylinder, the 
steps at their front ends curved to the cylinder. Elevation from plan and unfolding the centre line of 
wreath, showing the length of each baluster under the wreath. The wreath to be worked in three pieces. 
Drawing the face-moulds. See Plate 6 , Fig. 8 . 


PLATE 52. 

Plan of open-newel steamship stairs with platform and wing flights. The newels at the starting to 
continue above the upper deck and receive the level hand-rail and enclosing balustrade. Elevation from 
plan of curve and unfolding the centre line of wreath. Drawing the face-mould. 


PLATE 53. 

Hand-rail over a circular flight of stairs starting with a newel. Plan of stairs given on Plate 7, 
Fig. 10 . Drawing the face-moulds. 


PLATE 54. 

Plan for starting the circular stairs given on Plate 53 , with a scroll step and scrolled hand-rail in 
place of a newel. Construction of block for scroll step and riser. Scroll step complete. Face-mould for 
hand-rail scroll. How to describe the scroll of a superior form and in a simple way. 


PLATE 55. 

Hand-rail over an elliptic flight of stairs. Drawing the face-moulds. See Plate 7, Fig. ii, for com¬ 
plete plan of the stairs. 


PLATE 56. 

Instructions for sliding face-moulds, or for placing them in position to plumb the sides of wreath- 
pieces. Squaring wreath-pieces. How to determine the least thickness and width of plank required to work 
a wreath-piece of any given shape of hand-rail. 


PLATE 57. 

Wholesale-store stairs. Panel-work enclosure. Construction of close front-string, paneled and capped. 
Management of newels and hand-rail. 


PLATE 58. 

Plan of the landing portion of a flight of stairs turning one quarter, with a quarter-platform and square 
corner-pieces like small low-down newels set in the angles, over which is carried a continued hand-rail, with 
ramp and goose-neck at the landing. Construction of close front-string. Elevation showing paneled front¬ 
string, corner-piece, balusters, and method of continuing the hand-rail. 

PLATE 59. 

Plan of quarter-platform open-newel stairs; top portion of flight. Elevation from plan, and details. 
Laying out the angle newels. 


PLATE 60. 


Plan of quarter-platform stairs turning one quarter. Turned angle-newels, with hand rail ramped and 
kneed. Elevation and details. 


PLATE 61. 


Design for newels, baluster, and close front-string. 


PLATE 62. 

Plan of stairs turning one quarter and arranged to avoid winders by curving the front end of steps, 
making the latter parallel, and securing a platform. Also by this plan with the small newel no twists are 
required. Elevation from plan, showing length of newel and its connections with string, rail, balusters, etc. 
See Plate 5 , Fig. 7 . 


XIV 


CONTEiVTS. 


PLATE 03. 

Design for newel, hand-rail, and balusters; also design and construction of close front-string. 


PLATE 04. 

Design for an open-moulded stair-string, balusters and hand-rail. The balusters to be screwed with 
square-headed lag-screws to the side of the string, and the heads of the screws covered with turned or 
carved rosettes. 


PLATE 05. 

Design and construction of close front-string, newel and balusters. 

PLATE 00. 

Design of a turned and carved newel, carved string, and balustrade. Design of spiral-turned newels 
and balusters, bracketed string, ramp, and goose-neck hand-rail. Plan and elevation of a half-turn platform 
stairs, the plan so arranged that the newels will be of equal heights from the platform. 


PLATE 07. 

Ancient staircase at Rouen, France. From the Moniteur des Architectes. 


PLATE 08. 

Interior view of a flight of stairs turning one quarter, with a platform at the starting two rises up, 
the platform ornamentally enclosed on one side with panel-work to match the hall wainscot, and above 
which and across the hall spindle screen panels between columns. 


PLATE 09. 

Interior view of a grand staircase and spacious, suitably-fitted hall. 


PLATE 70. 

Designs for newels. 

PLATE 71. 

Designs for newels. 

PLATE 72. 

Designs for newels. 

PLATE 73. 

Sections of hand-rails of various forms and full size. 


PLATE 74. 

Sections of hand-rails of various forms and full size. 


PLATE 75. 
Newels and balusters. 


PLATE 76. 
Newels and balusters. 


PLATE 77. 
Newels and balusters. 


PLATE 78. 
The Tangentograph. 





STAIRS. 


Primitive man had little use for stairs; living in a hole dug in the ground, or a hut built of 
the branches and leaves of trees, or a log cabin, the utmost of his wants were doubtless supplied 
with a rude ladder. 

“We know little of the staircases of the Greeks and Romans, and it is remarkable that Vi¬ 
truvius* makes no mention of a staircase as an important part of an edifice; indeed, his silence 
seems to lead to the conclusion tliat the staircases of antiquity were not constructed with the 
luxury and magnificence to be seen in more recent buildings. The best-preserved ancient stair¬ 
cases are those constructed in the thickness of the walls of the pronaos —vestibules—of temples 
for ascending to the roofs. According to Pausaniasf similar staircases existed in the temple of 
the Olympian Jupiter at Elis. They were generally winding and spiral. Sometimes, as in the 
Pantheon at Rome, instead of being circular on the plan they are triangular. Very few ves¬ 
tiges of staircases are to be seen in the ruins of Pompeii, from which it may be inferred 
that what there were must have been of wood, and moreover that few of the houses were 
more than one story in height. Where they exist, as in the building at the above place 
called the country-house, and some others, they are narrow and inconvenient, witli rises some¬ 
times a foot in height. ... In modern architecture the magnificence of the staircase was but 
tardily developed. The manners, too, and the customs of domestic life for a length of time 
rendered unnecessary more than a staircase of very ordinary description.” J 

In England, all staircases preceding the latter part of the reign of Charles the Second 
— previous to 1660 — were either stairs winding round a post, or the strings were framed 
into square newels without balusters, but close-boarded, sometimes plastered between the rail 
and steps. Fig. i is an example built about 1557 of the close-boarding, pierced as the style 
began, and introducing afterwards a variety of designs. Later the flat-moulded baluster was 

introduced, as shown by Figs. 2, 3 and 4, and the carved balustrade, shown at Fig. 5. As the 

turning-lathe—a new invention of that time—came into use, turned balusters and newels were 
adopted, an example of which is given at Fig. 6. 

At Fig. 7 is. given an example of an ancient English tower staircase from Naworth Castle, 

Cumberland, England. 

In other parts of Europe the state of the art in all probability had not progressed beyond 
the examples here given. With the advancement of the arts and the enormous increase of 
wealth many costly and magnificent staircases are now built in private dwellings of the people 
of Europe and America. Of public buildings, a staircase in “ Goldsmiths’ Hall,” London, Eng¬ 
land, is said to have cost $150,000. At Washington, D. C., in the new hall of the House of 
Representatives, is a costly staircase built of stone with a highly artistic bronze balustrade. 
There are many elaborate and expensive staircases in the capitals of Europe that are impor¬ 
tant features of their public buildings. Iron and stone stairs are built on similar principles 
to those of wooden ones, the difference being in the treatment and changes required by the 
materials. 

When the first fashion of continued hand-rail called for the skill of the workman, 
the method adopted was that of bending and gluing together a number 
of thin wood veneers about a convex cylinder built for the purpose. The 
width of these veneers equaled the thickness of the rail, and the thickness 
of the veneers altogether made up the width of the rail, as shown by the 
accompanying sketch. The solid wreath of hand-rail formed in this way, 
after being allowed to dry,—which a writer observes “ took three weeks,” 

—was removed from the cylinder and carved into the shape of rail 
required. As late as the year 1826 instructions in the above method— 
although the author protested against it—were given in a book publfshed in England by 
M. A. Nicholson, entitled “ The Carpenter and Joiner’s Companion.” 

* Vitruvius, Marcus Polii, a Roman architect, 15 b.c. f Pausanias, an ancient Greek writer, 170 A.D. 

X Gvvilt’s Encyc. of Architecture. 









































'i'/nm 



XVI 




































































































































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j 

i' 



FlO. 6 


XVII 






































































































































































































DEFINITIONS. 


Stairs. —That mechanical structure in a building by which access from one story to 
another is obtained. 

Staircase. —The whole structure, consisting sometimes of a number of connecting flights of 
stairs, and again of one flight only. 

Well-hole. —The opening required for a complete staircase. 

Right-hand and Left-hand Stairs. —A stair is called right-hand if, when a person is going 
up the stairs, the hand-rail is on the right; but if in going up a stair the hand-rail is on the left, 
then the stair is called a left-hand stair. 

The Run of a flight of stairs is the horizontal distance from the first to the last riser in the 
flight. 

Tread. —The horizontal distance between two risers. One of the equal divisions into which 
the run of a flight is divided. 

Height of Story. —The vertical distance from the top of one floor to the top of the floor of 
the story above. 

Head-room. —Height required to clear the head in ascending or descending stairs. 

Rise. —The vertical height between two treads—one of the equal divisions into which the 
height of a story is divided. 

Riser. —The board forming the vertical portion of the front of a step to which it is glued 
or otherwise fastened at right angles. 

Step. —The horizontal plank upon which we tread in ascending or descending a stair. 

Nosing. —The outer or front edge of a step. It usually projects beyond the face of the 
riser a distance equal to the thickness of the step, and is rounded or moulded. 

Winders. —Steps of a triangular form in plan required in turning an angle or going 
round a curve. 

Scroll Step. —A bottom step with the front end shaped to receive the balusters round 
the scroll of the hand-rail; also called a Curtail Step. 

A Flight . —One continued series of steps without a landing. 

A Landing. —A horizontal resting-place at the top of any flight. 

A Half-turn Platform. —A landing extending across^ the well-hole, embracing the widths 
of two adjoining parallel flights as they land on and start from the platform. 

A Quarter Platform. —A square landing, the sides of which each equal the width of its 
connecting flight. 

Wall-string. —The string secured against the wall. A plank prepared by mortises sunk 
into its face to receive and house the ends of steps and risers on the wall side. 

Front-string. —The string on that side of the stairs over which the hand-rail hangs; a 

plank prepared and sawed out to receive and support the front ends of steps and risers. 

Open-string. —Same as front-string. 

Close Front-string. —A front-string into which the ends of steps are housed the same 

as a wall-string, the upper edge of the string capped to receive balusters ; and its outer 

face paneled or otherwise ornamentally finished. 

Pitch. —Angle of inclination. 

Pitch-board. —A piece of thin board in the form of a right-angled triangle, one of the 
sides of the right angle equal to a rise, the other side of the right angle equal to a tread 
of a stair. The hypothenuse is the pitch or angle of inclination of the s'tairs. 

Cylinder. —A concave semicircle, formed by gluing together hollowed wooden staves, or 
by bending over a convex cylinder. 

Quarter-cylinder. —A concave quarter-circle hollowed out of a solid piece of wood, or 
formed by being bent over a convex quarter-cylinder. 

Splice. —Half the thickness of wood cut away for a few inches of its length, so that it 
can be joined to another portion similarly treated. 

Facia. —A casing, finishing the face of beams—called headers—along the floor levels. 

Fillet. —A band -i\" wide by thick, nailed to the face of a front string below the cove 

or scotia, and extending the width of a tread ; and also a similar band mitred with the riser. 
The fillet is also nailed to the facia under the scotia along the levels. 

Curve-out. —A concave curve of the face of a front-string at its starting. 

Board. —Merchantable savved lumber of various widths and lengths, and one inch thick or less. 








DEFINITIONS. 


XIX 


Plank. Merchantable sawed lumber of different lengths and widths, and more t/ian one inch 
thick. 

Timber or Beam.— Sawed lumber of large size. 

Carriage-timbers.— Permanent timber supports nailed under stairs parallel to the lower 
edge of strings. 

Newel. —An ornamental post or column—built or turned solid—of various sizes and 
designs, set at the foot of stairs to receive and secure the hand-rail. In open-newel stairs, 
posts of a small size set at the angles and into which the strings are framed. 

A Straight Flight of Stairs —Is one in which all the steps are parallel and at right 
angles to the strings. 

Quarter-turn W^inding Stairs. —A stairs in which the winders make a turn of one quarter 
to a landing or to a continuation of the flight. 

Half-turn Winding Stairs. —A stairs in which the winders make a turn of one half to a 
landing, or to a continuation of the flight. 

Circular Stairs —Are stairs with steps planned in a circle, toward the centre of which 
they all converge, and consequently are all winders. These stairs may have a circular, a 
square, or octagonal-shaped wall ; and on the front an open cylinder and continued hand¬ 
rail, or a solid circular post with the front ends of steps and risers housed into the post. 

Elliptic Stairs. —Stairs that are elliptic on the plan. The treads are spaced on the front 
and wall strings, but being less in width on the front-string, they all converge, but not to 
one centre like those of a circular stairs. 

Newel Stairs. —Stairs in which newels are substituted for cylinders and continued hand¬ 
rail. 

Open-newel Stairs —Are so called because they have small newels arranged at the 
angles of an opening in place of cylinders. The connecting front-strings are framed into the 
newels, 

Hand-rail. —A variously-moulded form and size of rail running parallel to the inclination 
of a stairs, and usually kept at a vertical height of 2'.2" from the top of step to the bottom 
of rail, at the centre of short balusters. The rail also continues around cylinders, or connect¬ 
ing with newels parallel to floor levels, at a height of 2'.6" * from floor to bottom of rail. 

Baluster. —A small column made of different forms and sizes, but commonly turned. 
They are set vertically on the steps of stairs, generally two on a step, and placed the same 
distances apart on the floor levels, forming an ornamental enclosure and furnishing support 
for the hand-rail. 

Balustrade. —Balusters and hand-rail combined. 

Wreath. —The whole of a helically-curved hand-rail, whether it makes a half-revolution 
or more. 

Wreath-piece. —A portion of a wreath less than the whole. 

Face-mould. —A section produced on any inclined plane vertically over a curved plan of 
hand-rail; including also in the same plane with the face-mould tangents to a central curve¬ 
line of the plan. Joints of face moulds are made at right angles to these tangents. 

Ramp. —A concave or convex curve or easement of an angle, as sometimes required at 
the end of a wreath, and the adjoining straight rail, where the two have different inclinations- 

Ramp and Knee. —A concave easement of hand-rail with its upper end forming an angular 
knee. When the knee is curved convex the combined curves are called a Swan-neck. These 
two forms—ramp and knee, and ramp and swan-neck—are used in open-newel and other 
stairs where the newels are turned. 

Butt-joint. —An end joint made at right angles to the central tangent of a wreath-piece; 
and also an end joint made at right angles to any straight length of hand-rail. 

* In figuring measurements of architectural drawings, and in specifying sizes, feet and inches are designated by accent- 
marks—called indices — as follows ; 2'. 6 " meaning two feet six inches. Feet are denoted by one accent-mark over 

the number, and a period on the right separating it from the fractions of a foot,—inches Inches have two accent- 

marks over the number as shown. Feet and no inches are indicated thus: 25'.o"—twenty-five feet no inches ; inches 
and no feet thus; o'.6"—no feet six inches. The latter is frequently written with the indices for inches only, as 6". 








BOOKS PUBLISHED TREATING ON STAIR-BUILDING. 


The following is a complete list and dates, as far as ascertained, of publications in the 
English language that either treat partially or wholly of stair-building and hand-railing ; 

Date. 

1693. Moxon, “ Mechanical Exercises.” 

1725. Halfpenny, “ Art of Sound Building.” 

1735 - Francis Price, “ British Carpenter.” 

1738. Batty Langley, “ Builder’s Complete Assistant.” 

1750. Abraham Swan, “Architect.” 

1792. Peter Nicholson, “ Carpenter’s Guide.” 

1813. Peter Nicholson, New “Carpenter’s Guide.” 

1826. M. A. Nicholson, “ Carpenter, Joiner, and Builder’s Companion.” 

1864. Joshua Jeays, “ Orthogonal System of Hand-railing.” 

1873. Newland’s “ Carpenter and Joiner’s Assistant.” 


The above are all English publications. The following are all—or have been—published 
in the United States : 

I 

Date. 

1844. R. G. Hatfield, “ The American House-carpenter.” 

1845. Simon De Graff, “ The Modern Geometrical Stair-builder’s Guide.” 

1849. Cupper’s “ Hand-railing.” 

1856. Robert Riddell’s “ Hand-railing.” 

1858. Perry’s “ Hand-railing.” 

1859. Esterbrook & Monckton’s “American Stair-builder.” 

1872. Monckton’s “National Stair-builder.” 

1875. Gould’s “ Hand-railing.” 

1887. Monckton’s “ Stair-building in its Various Forms, and One Plane Method of Drawing Face 
Moulds and Unfolding the Centre Line of Wreaths..” 



SUGGESTIONS. 


The Attention of Teachers Engaged in Giving Instruction in Architectural Drawing 
in Technical Schools is Invited to the Examination of this Work, which is believed to be 
well suited for taking up an important part of interior use and decoration—the planning and 
construction of stairs, a branch of building but slightly touched, while roofs and other parts of 
building structures are taught in much detail. 

Apprentices who desire to master the contents of this book are informed that much care in 
its preparation was given to make the whole so simple and clearly stated, that it would be easy 
to learn ; yet if any have had no previous practice in the use of drawing-instruments, and no 
knowledge of piactical geometry, such should at once begin that study. A notice of a little book of 
Practical Geometry, treating; likexvise of the use of instruments and all the necessities of a beginner in the 
study of drawing, will be found in the last pages of this work. 

In the Study of Hand-railing the paper formed solids beginning with Plate No. lo should 
be drawn as directed, cut out, and glued in shape as explained ; for this purpose a little bottle 
(with brush) of LePage’s liquid glue is best and most convenient. 

The Squaring of Model Wreath-pieces, one quarter of full size—or one half size in case 
of small cylinders—out of some soft wood brings valuable results to the apprentice, of which the 
first is Practice; second. Experience; third. Knowledge. 

Fitting Wreaths over Circular or other Curved Iron Staircases. —Begin by chalking on 
the iron hand-rail plate suitable lengths of wreath-pieces; and to get a parallel pattern for each 
of these pieces, press a thick, strong sheet of paper to the top of the plate, and mark the concave 
and convex edges of the plate as far as the length requires; parallel to the curves thus marked 
set off each siile enough to make the width equal that given by trial at Figs. 6 or 7, Plate No. 
56, and a half-inch more each side of the centre; but make the thickness of plank as found at the 
last-mentioned plate and figures; cut the paper joints to suit the eye, and a little long. These 
paper patterns are used to mark the shape of the wreath-pieces on the plank; they are then sawed 
out square through. The bottom of the wreath-piece is first fitted to the iron plate and the plate 
let in flush ; then plumb-lines are put on the joints, the sides worked plumb and brought to a 
width; lastly the top is cut away to the thickness, and the joints finished; when the adjoining 
pieces are squared, their joints are fitted against the first piece, etc. 

Note. —Fitting wreaths over iron staircases on iron rail plates is done as above directed becatise the 
curves to which the iron is brought are often various and eccentric, consequently fitting is resorted to as 
quickest and best. 

Self-supporting Circular Stairs are rarely built. These stairs stand disconnected and away 
from walls or any points of support, except at the top and bottom, and have hand-rails and balusters 
over both strings. No carriage-timbers need be used if the risers are increased in thickness and 
the strings are made thick and bent laminated as explained at Plate No. 8, Fig. 5. The strings 
at the bottom should be run down between the floor-beams and secured with strong iron bolts ; 
they should also be strongly bolted at the top. Only screws ought to be used on such a stair¬ 
case. Jib panels should be built as high as can be permitted under the strings at the foot of 
the stairs. The management of hand-railing for circular stairs is given at Plates Nos. 53 and 54. 

Close Paneled Strings are best suited to neweled stairs, but if this construction is used 
with cylinders they should be of large diameter, otherwise the work will appear cramped and 
uglv. 

The Joints of All Wreath-pieces with the exception of those given at Plates No. 34 
and 35 must be made at right angles to the face of the plank. 

Newel Caps Mitred to Hand-rails ought to be abolished. 

Turned newels should be finished in one solid piece. The connection of hand-rail with newel 
is stronger and better if run straight to the newel and bolted together. 

Balusters with Square Bases insure a stronger balustrade than those with circular bases. 

Hand-rails may be Finished and Varnished before being set up, if reasonable accuracy 
be observed in the drawing and in the work. 



PLATE 1. 


Plan and Elevation of a Straight Flight of Stairs with a Seven-inch Cylinder; 
ALSO A Plan and Elevation of a Platform Stairs with a Six-inch Cylinder Land¬ 
ing WITH Four Rises Above the Platform. 

Fig. I. Plan of a Straight Flight of Stairs. —The plan is given to show the width of the stairs, 
the size and position of the cylinder, the number and position of the rises and treads ; also by means of the 
shaded lines to show the opening of the well-hole, its width and length ; its width sufficient to receive the 
width of stairs, the diameter of cylinder and the thickness of facia ; its length sufficient for head-room. 

Fig. 2. Elevation of the Straight Flight of Stairs Shown by Plan at Fig. i. The 
number of rises is determined by dividing the height of story—taken from the top of the floor of the 
lower story to the top of the floor in the upper story—into any number of suitable parts ; in this case the 
height of story is io'.4", equal to 124”, which divided by 16 gives a quotient of 7^”, the height of one rise. In 
the above manner the height of any given story must be taken and divided into any number, more or less, of 
rises. The rod E F shows the manner of taking the height and the division of rises. To obtain the tread,* 
first find the horizontal distance that can be taken for the run of the stairs and landing room ; which in this 
case is equal to A D, 14'.5”; of this the landing room, B D, must never be less than the width of the stairs, and 
is always better several inches more ; therefore take B D, 2'.9”, for landing, and C B, 5”, for depth of cylinder ; 
leaving AC, ii'-s", to be divided into treads. There is always one tread less than the number of rises in each 
flight of stairs, because the floor itself becomes a step for the top rise ; so having sixteen rises in this flight, 
the remaining equal to 135”, must be divided into fifteen parts, which equals g" for each tread, 

as shown at plan and elevation. The line G H is the lower edge of the string-plank, which plank is sawed out 
to receive and make a finish with the risers and steps. The dotted lines parallel to G H indicate the position 
of the supporting carriage-timbers. Head-room is secured by constructing the well-hole of a sufficient length 
so that the tallest person in ascending or descending the stairs would not be in danger of striking the 
head. Head-room should not be less than 7'.o". It is not necessary to draw an elevation of steps and rises to 
determine head-room, for that can be learned from the plan at Fig. i ; for example, count thirteen rises from 
the top down at J ; thirteen rises, 7^"each, equal 8'.4^” ; subtract from this the thickness of floor, depth of 
beam and plaster, altogether 10^", and there will remain 7'.6" ftsr head-room,—if the length of the well-hole 
does not cover the step J, Fig. i. 

Fig. 3. Plan of Platform Stairs. —Platform stairs ascend from one story to another in two or 
more flights, having platforms between for resting and changing their direction. This plan has but one plat¬ 
form, taking the whole width of the hall, and has four rises in the upper short flight and thirteen rises in the 
lower starting flight. The shaded lines show the framing of the open well-hole, including the platform. 

Fig. 4. Elevation of Platform Stairs from the Plan Fig. 3. —I J is the height-rod showing 
the division and number of rises. 

The head-room and tread are found as before explained at Fig. 2. Some attention must be given to 
the position of platform K, so that the height underneath has sufficient head-room and clears the trim or fan¬ 
light of doorway, if there be any ; for the platform may be one or more rises higher if space can be spared to 
add one or more treads to the starting flight—these treads to be taken from the short landing flight. At L 
is shown the starting of a second flight from that floor. 

A Rule to Find the Correct Proportion of Tread to Rise. —To any given rise in inches add 
a sum Uiat together will equal twelve, double the sum added to the given rise for the tread in inches,—as 
follows : given a 5" rise and 7 make 12, then twice 7 equals the required tread, 14”; or again, given a 7" rise 
and 5 make 12, then twice 5 equals the tread, 10", etc. 


* The tread is the distance between risers, as M N Fig. 2, without including the projecting nosing ; when the projection of the 
nosing is added the whole is called the step. The projection of the nosing is usually made equal to the thickness of the step. 















































































































































































































PLATE 2. 


Stepladders and Stoop. 

Fig. I. Plan of Stepladder. —This plan shows the thickness of the sides, the width of the ladder, 
the treads and number of rises, also an extra width of tread, as at P Q, which should always be allowed at 
the top step of a ladder. 

With P Q, 3^” deducted from the run P M, there remains Q M, equal to 3'.6^”, or to be divided 

by lo, the quotient of which is 4^", the tread. The point of the ladder N M, if desirable, may be cut off on 
the line N 0 , and glued and nailed to the back edge of the ladder, keeping the point V to the floor. 

Fig. 2. Elevation of Stepladder given at Plan Fig. i. —The height from floor to landing 
above is which divided by lo gives a quotient of 9^", the height of each rise. The sides of step- 

ladders having from ten to fifteen rises should be from 5" to 7” in width and not less than thick. One 
way to lay out the sides of a stepladder is as follows : let T R equal the tread and R S the rise ; connect 
T S : take the distance T S in the compasses and mark on the edge of the side of ladder from V to A ten spaces, 
and with a bevel (as at X taken from T) lay out the angle and thickness of steps as shown. Another way to 
lay out the sides of a stepladder is to use a steel square (^as at B), placing the square at the edge of the ladder 
to the height of rise and width of tread as figured on the square and as many times as there are to be rises in 
the ladder. The steps should be let into the sides of a ladder from y^" to yy ; y^" will be sufficient if the 
sides are i” thick. 

Steps are set into the sides of a ladder (as at Z Y) when the sides of ladder are 9" or 10” wide and 2" or 
3" thick, as sometimes built in buildings used for wholesale stores. 

To make a small movable stepladder strong and keep the steps from working loose a tenon should be run 
through the sides at three points (as at i, 2, 3) and properly nailed. 

Figs. 3 and 4. Plan and Isometrical Elevation of a Double Stepladder. —Where space 
is limited and only occasional communication between stories is necessary, this ladder will answer the 
requirements, as it can be constructed in the cheapest manner-and put up in mere closet-room. Hand-rails 
should be put up at both sides of the ladder, hung on iron brackets well secured in the wall, by the plan at 
Fig. 3 and its perspective. At Fig. 4 there are shown fifteen rises of 8" each, making a total height of 
10'.o”; and fourteen treads of 9" each, occupying a run of 5'.3''. 

Fig. 5 - Elevation of Stoop with Platform. —The newel-post and balusters have no turned work, 
but are cut on the angles and chamfered. 

The strings where there are so few steps may be laid out with a steel square, or can be laid out with a 
pitchboard in the same manner as inside stairs. Fig. 6 . A pitchboard, to be made of thin, well-seasoned 
wood, N M 0 , must be made perfectly square, M N the tread and M 0 the rise. The grain of the wood 
should always run in the direction of N 0 . The edge of the string C should be jointed, and a pencil-gauge 
distance equal to C D run along from the edge C. 

The distance C D is equal all together to depth of timber, thickness of ri.ser, and thickness of ceiling 
boards underneath. Along the line C the pitchboard is marked on the stuff as many times as there are to be 
rises, and then sawed square through on the line of treads, and cut mitring on the line of rises. The dotted 
lines show the correct position of the hand-rail to determine its exact length ; the platform level rail is raised 
4" above the platform, so that when the rail at the centre of the short balusters along the flight is raised the 
usual height, 2'.2", the level rail over the platform will be 2'.6'', the usual height for a level rail. At the 
newel G H is raised 3>^'', which added to 2'.2”—the height at the centre of the short balusters—makes the 
height G K at newel 2'.5^”. 


Note.— The whole of the above practical details and directions 
similar work is required. 


relating to an ordinary stoop apply equally to inside stairs where 







P LATE N 0. 2. 

































































































































































































































































PLATE 3. 


Plan, Elevation and Details of a Common Straight Flight of Stairs.—Stair-building 

Generally. 

Fig. I. Plan of a Common Straight Flight of Stairs ; showing the width of the flight, the 
thickness of wall-string, the width of treads and number of treads and rises, the position of the balusters, the 
cylinder, the width and place of hand-rail and size of newel-post. 

Figs. 2 and 3. Methods of Forming Cylinders and Splicing them to Strings. 

Fig. 4. Wall-string Laid Out, showing easements of angles joining floor-base at starting and landing, 
mortises laid out with wedge-room for steps and risers which are to be let into the string . 

Fig. 5. Front-string Laid Out.— A B must be sufficient for depth of timber, thickness of plaster 
and of riser. The dotted lines at C show the wood to be left on the string for cylinder-splice. G F H D E 
is the cylinder opened out; F G must be the depth of floor-beam and thickness of plaster ; the line D E G is 
the bottom edge of the cylinder, and at E the curve is raised somewhat above the direction of the line A D in 
shaping the edge, so as to prevent a baggy appearance the cylinder would otherwise have when in place. 

Fig. 6. Step and Riser as Glued Together.— The whole thickness of the riser is let into the 
ploughed groove of the step ; J is a glue-block, of which two or more are glued and nailed in place as shown 
along the length of step and riser. K K are dovetail mortises cut in the end of steps to which the balusters 
are fitted, glued and secured in position as shown at Fig. 8. The step and riser are backnailed together as at 
R ; from two to four nails are driven in, depending on the length of steps. 

Fig. 7. Stair-timbering and Rough-bracketing. —This drawing represents a vertical section 
cut through the middle of a flight—a plan of which is given at Fig. i— showing an end view of steps and 
risers, rough board brackets L L, the middle timber M, and piaster N. Stairs 3'.o" wide and less are usually 
provided with two carriage, or supporting, timbers, one of which is used to strengthen the front-string, this 
string being securely nailed to the timber ; the other timber, M, is placed at the centre of the stairs and rough 
board brackets, L L L, fitted and nailed as shown at alternate sides of the timber. At S the nail through the 
rough-bracket is driven into the back of the step. 

Fig. 8. Side Elevation of the Starting Portion of Stairs, a Plan of which is Given at 
Fig. I.— T he hand-rail is brought straight to the newel at Q, as being a-stronger and better connection in 
many ways than the old plan of a loose turned cap and easement of rail mitred to the cap. P is a jib panel 
which is usually made as a finish to the bottom of a first-story flight, and also to receive the level rail, 0, that 
encloses the basement-stair well-hole. There is no better or stronger method of building w'ooden stairs than 
what is here described in detail, where each step and riser are glued together in the manner shown at Fig. 6, 
and housed and properly wedged with glue and hard-wood wedges in the wall-string, as shown at Fig. 4,— 
also housed and wedged in the same manner at the front, if a close front-string is used. Carriage-timbers, 
rough-bracketed as before described at Fig. 7, of a size from 2" by 4” to 4” by 10", and from two to five 
timbers—never less than two—to each flight, depending on the width and extent of the stairs and the weight 
they are expected to carry. 

For good substantial work well-seasoned materials should be used throughout. So important is this con¬ 
sidered in the larger-sized timber that old second-hand timber is sometimes sought for. Whole flights of 
stairs—with the exception of circular, elliptic, or some other peculiar form—are most economically finished by 
being wedged and nailed together, trimmed and raised to their places in the building complete ; the support¬ 
ing timbers are easily put in position afterward. Generally the staircase may be put up on the dry brown 
wall, and if made of hard wood the steps, risers, strings and newels may be completely covered with cheap 
heavy brown paper and thin rough boards, to remain as a protection until the walls are finished with white 
plaster, the doors hung, the mantels and grates set. 

This covering when put on may be so arranged as to enable the stair-builder to easily remove some six 
inches of it, enough to allow the hand-rail to be put up and finished, leaving the balance of the covering until 
no longer required. 

A Staircase of Any Form of Plan may be Finished on the Under Side, Showing its 
Construction with far more elegance and variety than any surface plastering or close panelling com¬ 
monly done. In this finish the wedged strings will have to be cased to conceal the wedging. Both the wall 
and front strings should have greater thickness than usual ; the front-string should be thick enough to 
dispense with a front carriage-timber, or such timber may be used and cased. If desirable the risers can be 
made of a thickness and strength that no middle supporting string or cased carriage-timber would be 
required : this would leave an unobstructed view of panelled steps and risers, or other ornamental finish. 

The Old English Method of Stair-building —which is occasionally followed in this city, and 
commonly in some portions of the United States—is to construct rough timber carriage-ways sawed out for 
step and riser, with rough steps nailed on, to be used for travel during the process of building, and to be 
plaster-finished as required on the under side, at the same time with the walls of the building. This carriage¬ 
way is then cased with finished strings, steps and risers ; the wall-string and sometimes the- rontfstring— 
where the latter is to be close—are scribed to the grooved step and riser and set in this groove with a 
tongue ; the projecting step nosing is sawed to fit against the face of the scribed string. This last method of 
building the bodies of staircases is not as good as the more modern one previously described, and is also much tnore 
costly. 






















































































































































































PLATE 4. 


Planning Winding Stairs—Drawing Elevation of the Same—Laying Out the Strings. 

Fig. I. Plan of a Staircase Winding One Quarter, Alike at the Top and at the Bottom, 
with Cylinders lO" in Diameter.—It is important in planning winding stairs of various forms—and this 
example will serve for all—to make the treads as nearly as possible of a uniform width on an established line of 
travel, which is about 14" from the front-string as shown. It is well to increase the width of the stairs a few 
inches both at the top and at the bottom, for the more convenient passage of furniture at these turns. In 
making the plan of stairs, the first thing to be determined is the wall-lines A BCD, next the width of the body 
of the stairs from the wall E to the front-string F. I'he width of the hall for this staircase will require to be 
7' between rough walls—3'.o" width of stairs, 10" diameter of cylinder, 3'.o passageway, and 2" thickness of 
plaster. From the walls to the cylinder, at both the top and the bottom of the stairs, the width is made ^'.2”. 
'i'he line of travel is drawn in position as before mentioned ; the starting or first and top or landing riser lines 
are now drawn as required, taking care that not less in any case than 2" level of the cylinders, as at X X, be 
left at both top and bottom so as to make a proper finish with the facias. Between these starting and landing 
risers, on the line of travel, equal spaces are marked for the width and number of treads required ; next the 
treads in the cylinders and along the line of the front-string are marked as figured ; now the lines of risers 
are drawn from the points of division at cylinders and front-string, through the points of division first made 
on the line of travel : and this completes the plan. 

Fig. 2. Elevation of the Plan of Stairs, Fig. i.—This elevation explains itself in connection 
with the plan beneath : The important points given by the elevation are the head-room from the top of the 
third step, G, to the plastered ceiling, H, and the length of the well-hole as limited and shown by the line G H. 
It is not necessary to set up an elevation of a staircase to fix the head-room. The head-room may be deter¬ 
mined, and the length of well-hole, by finding how many rises down from the top—after subtracting therefrom 
the depth of floor-beam, including floor and plaster—would equal in height y'.o", or very nearly that. 

Fig. 3. Laying Out of the Front-string and Cylinder. —The dista^nce K J, on the front-string, 
must equal all together the depth of timber, thickness of plaster and thickness of riser. The cylinders are 
spliced to the string on the lines 0 P and R S ; the treads, as given in the cylinders and string, agree with the 
plan Fig. i. At the starting cylinder, N X equals 10", the width of facia, which is the depth of,floor-beam (9”) 
and thickness of plaster (i"). The top cylinder requires a straight piece of board the thickness of facia 
glued at its upper end, of sufficient width and length (as at T X V U) to produce an easing between the lower 
edge of the cylinder and the lower edge of the facia ; this piece is glued to the cylinder on the line T X, and 
joins the facia on the line U V. The depth to the lower end of the cylinders is found, as shown, by describing 
arcs of a radius equal to K J from the angles of tread and rise as shown at Q 0 and W T. It is better to 
join the cylinder as at R, on the straight line R K, even if it has 2" or 3" more depth at that point than at K J. 
Cylinders are sometimes—generally in the best work—laid out with the straight string in 07 ie plank^ as here shown, 
and the whole of that portion for forming the cyli 7 iders tip to the lines 0 P a 7 id R S is cut away at the back, leaving 
only a thi 7 i ve 7 ieer at the face, which is bent over a co 7 ivex cylinder a 7 id filled out with staves, as described at Fig. 4, 
Plate 8. 

Fig. 4. Wall-String.—This string is the starting portion, A B, at the plan Fig. i. In preparing this 
string to join the floor-base, V S is the height of base, then S L is the easing of the angle of string to the 
level of the base ; or the string may be mitred to the base, as at Y 0 , R Y being equal to V S. The height of 
string M N above the angle-step must be alike from the same step as M N at the next string. Fig. 5 ; also the 
strings connecting at these angles may be brought to a level, curved as shown, or left angular ; but they 77 iust 
in all cases be brought to a level, so that the base- 7 nouldi 7 igs will prope 7 -ly connect. 

Fig. 5. Wall-string.—This is the whole of that portion of wall-string marked B C of the plan Fig. 
I. The height of the string at 0 P must be alike from the same angle-step as at 0 P of Fig. 8. I'his string 
is laid out in two pieces spliced together at the centre, Z D ; it may be laid out in one piece by the use of a 
mean tread, and in another way, each of which methods will now be given. 

Fig. 6. Wall-string same as Fig. 5, Laid Out in One Piece by the Use of a Mean 
Tread.—A mean tread is found by adding together the ten treads as figured, and dividing their sum by the 
number of rises (9), as follows : 25-1-17-p 13 4-9 4-9-f 9-p9-f 13-f 17 + 23^ = 144^-^9= 16-g'^-p " mean tread, 
which is nearly 16^". Along any line, A B, beginning at A, apply the mean tread, A C, and the rise, C D, as 
shown, marking each tread in their order of the width required, and if the work has been correctly performed 
the last tread, 25", will come out at B of the line A B. 

Fig. 7. To Lay Out Winder-strings from a Scale Drawing.—Set up to a scale of \yf' to i' 
an elevation of treads and rises the same as at Fig. 6, and draw a line touching the outermost points of the 
upper edge of string, as X E 0 ; then with a bevel set to the angle Q 0 S a string may be laid out full size 
whose points X and E will touch the edge of plank. Begin laying out with the line 0 S, and make 0 S as 
many inches full size as it measures on the scale. 

Fig. 8. Wall-string.—This string is the landing portion of wall-string marked C D on the plan Fig. i. 






























































































































































PLATE 5. 


Through the drawings given in this plate and the two following plates, over thirty different plans of stairs 
are presented ; they are all made to a scale and figured for convenient reference. These various plans are 
intended to afford opportunity for the examination and study of stair plans, properly arranged for their 
different requirements. The grading of treads next to the cylinder in the case of winders, so that the wreath 
will make easier curves and less inclinations in its connections, is a matter of no slight importance. A little 
more attention, a better knowledge of practical details in planning stairs, will often lead to saving valuable 
space, or to a more comfortable passage from floor to floor. A superior plan of stairs may even prove to be 
a question of humanity ; a cruel thing it may be to a little child or an aged and feeble person to subject them 
to the danger and discomfort of travelling over oblique winding steps; as, for example, at Fig. 5, when a very 
little more space, as figured, will permit a safe and ea.sy stairway for all, as shown at Fig. 6 . 

Fig. I. Plan of a Straight Flight of Stairs Starting and Landing with Small Cylin¬ 
ders. —The position of cylinders with regard to starting and landing risers, as shown in this case, is 
explained in detail at Plate No. 22, Figs, i and 2. 

Fig. 2. Plan of a Straight Flight of Stairs Starting with a Newel Set-off 2 ) 4 " and 
Landing with a 7" Cylinder; the Landing Riser Set Into the Cylinder 2 }^".— The set-off of 
a newel and its management in connection with the hand-rail is given at Plate 31, Figs, i and 2. The cylin¬ 
der at the landing is treated in detail at Plate 33. 

Fig. 3. Plan of Winding Staircase with Mortised Strings Both Sides. —These stairs are 
only used where room for better cannot be spared, in such places as an attic or basement story. A and B 
are plank continuations of string 5" wide and long enough when spliced to the mortised string at the top and 
at the bottom to receive the winding steps and risers, which wall be better understood by examining the 
elevation of string set up at Fig. 4. 

Fig. 5. Plan of the Top or Landing Portion of a Quarter-turn Winding Stairs, with a 
Small Cylinder. —The management of the hand-rail of this case is given at Plate 25. 

Fig. 6. Plan of the Top Portion of a Staircase Turning One-quarter to the Landing, 
with Diminished Steps Around the Cylinder; Curved Risers and Platform. —This plan is an 
improvement on that given at Fig. 5. By curving the risers, winders are avoided and a roomy platform 
secured with the same small cylinder. But with the number and width of treads alike, this plan requires 7^” 
more room, as shown at C D. The hand-rail of this case is treated in detail at Plate 26. 

Fig 7. Plan of the Top Portion of a Staircase Turning One Quarter with Diminished 
Steps, Curved Risers, Newel and Level Quarter-cylinder, and Platform. —In this plan a small 
newel is introduced with a connecting level quarter-cylinder ; designed to take the place of plan Fig. 6, where 
this is preferred. By this plan no wreath or ramp will be required. A design of neioel; the plan, elevation and 
management of this case in detail will b'e foimd at Plate 62. 

Fig. 8. Plan for Starting or Landing of a Staircase. —By using a single newel and setting it 
diagonally, as shown, it will be strong in all of its connections. In some styles of interior finish this position 
of newel would be desirable. 

Fig. 9. Plan of Stairs (Combining Two Platforms with Curved Risers Between) 
Making a Half-turn. —The management of the hand-rail for this plan of stairs is given in detail at 
Plate 41. 

Fig. 10. Plan of a Platform Stairs Making a Quarter-turn with a Quarter-cylinder.— 

Whatever radius is taken for the quarter-cylinder in this description of stairs, in order to make the best form 
of wreath-piece, from E, the centre of the hand-rail, to risers F and G must be each half a tread. See Plate 
37, Figs. 5, 6 and 7. Also Plate 45, Fig. i. 

Fig. II. Plan of Stairs Turning One Quarter with Winders and a Quarter-cylinder.— 

In planning this kind of staircase experience has proved that the best shaped hand-rail is produced by 
bringing the rail at the upper portion, K, straight into the wreath-piece at the end without a ramp, for this 
reason : one winder at K, above the quarter-cylinder, is all that should be allowed. See Plate 36. 


Plate No. 5. 


























































































































































































PLATE 6. 


Fig. I. Plan of Platform Stairs with the Risers at the Platform Set Into the Cylin¬ 
der All that can be Profitable. —Placing the risers in the position given on the plan saves 6" at both 
the landing and starting flights connected with the platform. The management of the hand-rail is given at 
Plate No. 38. 

Fig 2. Plan of a Winding Staircase with 10” Cylinders, Making a Half-turn at Each 
Cylinder.—The hand-rail for this plan is treated in full detail for the top or landing portion at Plate No. 
28, and for the starting at Plate No. 29. 

Fig. 3. Plan of a Winding Staircase, Two Flights Connecting with a 12" Cylinder.— 

The details and treatment of hand-rail are given at Plate No. 42. 

Fig. 4. Plan of Stairs with Newel Set Between Two Quarter-cylinders.— In this case the 
treatment of hand-rail, if at the top of a flight, will be substantially the same as that given at Fig. 2 of 
Plate No. 24, and if at the starting of the flight. Fig. i of Plate No. 24. 

Fig. 5. Plan of the Starting of a Staircase. —Where the hall is wide enough and it is desirable 
to make the flight broad and inviting, the front-string is curved out, embracing four or five treads. This case 
of hand-rail is treated at Plate No. 30, Figs, i, 2 and 3. 

Fig. 6. Plan of Platform Stairs with Low-down Small Corner Newels and Continued 
Hand-rail. —A design and the management of stairs and hand-rail of this plan are given in detail at 
Plate No. 58. 

Fig. 7. Plan of Platform Newelled Stairs with Wing-flights. —This staircase, suitable for a 
very large hall of a public building, is designed to be wainscoted and with half-newels at the walls, as shown, 
running through and ornamentally finished at the under-side of the stairs. The best effect given to a stair¬ 
case of this character is by showing the whole open construction of the under-side, tastefully finished, free from 
plaster or close soffit panelling. 

Fig. 8. Plan of Stairs Making a Half-turn, with a Large Cylinder Filled with Treads 
of Equal Width to those of the Straight Portion of the Flights, and Curving the Ends 
of the Risers so as to Avoid Winders and Secure an Ample Platform. —Full detail instruction 
for the management of the hand-rail over this plan is given at Plate No. 51. 

Fig. 9. Plan of Staircase Suitable for Steamboat or Ship, where Every Inch of Space 
is Valuable.—The requirements of a hand-rail over this plan are treated in detail at Plate No. 50. See, 
also, Plate No. 52. 


p 


No. 6. 



Fig.1. 






Fig.4. 



Fig.5. 




L 

i 













































































































































































































































PLATE 7. 


Fig. I. Plan of Platform Stairs. —By placing the risers six inches into both cylinders as seen in 
this plan, that amount of room is saved in each case—a matter of saving that is sometimes of much impor¬ 
tance. The treatment of the hand-rail over this plan is given at Plate No. 40. 

Fig. 2. Plan of Double Platform Stairs Made by Introducing a Riser at the Centre of the 
Cylinder.— The treatment of the hand-rail over this plan is given at Plate No. 39. 

Fig. 3. Plan of Winding Stairs Making a Three-quarter Turn.— The management of the hand¬ 
rail over the centre cylinder of this flight is given at Plate No. 47, and over the starting portion at Plate 
No. 48. 

Fig. 4. Plan of a Quarter Platform Stairs.— By curving risers in the manner here shown, a good 
roomy square stepping plan is made of what would otherwise be winders ; somewhat like those of plan at Fig. 
6. The details and management of hand-rail over this plan will be found at Plate No. 46. 

Fig* 5 * Plan of a Quarter Platform Stairs with Newels Set in the Angles. —The framing of 
these newels and their connections of hand-rail is given in complete detail at Plate No. 59. 

Fig. 6. Plan of a Quarter-turn Winding Stairs at Starting.— The detailed instruction for 
the management of hand-rail over this plan is given at Plate No. 27. 

Fig. 7. Plan of the Top Portion of a Quarter-turn Winding Stairs.— The management of 
hand-rail over a plan similar to this will be found at Plate No. 26. This plan shows a way of curving the 
risers so as to save a sometimes much-needed space by lessening the distance from the wall B to the landing 
riser C. 

Fig. 8. Plan of a Quarter Platform Stairs Much the Same as that Given at Fig. 4, Except 
the Shape of the Cylinder. —The management of hand-rail over this plan is given at Plate No. 44. 

Fig. 9. Plan of a Quarter Platform Stairs with One Tread Placed at the Centre of 
the Cylinder.— Management and detail of hand-rail over this plan will be found at Plate No. 43. 

Fig. 10. Plan of a Circular Staircase.— The dotted lines show the best method of timbering a 
staircase of this or similar form. The practical treatment of hand-rail over this plan may be found at Plate 
No. 53 ; also at Plate No. 54 are given full instructions for changing the plan of the first step to the scroll 
form, the management of that portion of the hand-rail, also the construction of the scroll step. 

Fig. II. Plan of an Elliptic Staircase. —This plan has the treads on the line of wall and front 
strings graded so that the risers are placed in a direction nearly normal to the curve, keeping an even tread 
on the line of travel ; which would not be the case if the treads were made equal at the wall-string and 
at the front-string. The hand-rail over this plan is given in detail at Plate 55. 

Independent or Self-supporting Staircases.— This kind of stairs derives no support from wall 
or partition ; they are seldom required, but when called for are mostly of a circular plan. An independent 
straight staircase presents no difficulty ; for all that is required of it is, that it be well secured at the top and 
bottom, and that the material and construction have ample strength to support the weight it will be liable to 
carry. Where the plan of a self-supporting staircase is circular with an open well-hole as at Fig. 10,* the 
timbers at the foot of the stairs R Q P should be bolted to the floor-beams, and bolted at all their connections 
up to and including the floor-beams at the landing. Jib panels should be put in at the starting of both 
strings as high up as can be allowed ; or set up a supporting column near the centre of the flight. Or again, 
if it is convenient, let an iron bolt secured in an adjoining wall project sufficient to support the staircase at 
about the centre L. With the supports mentioned these stairs may be finished on the under side and made of 
sufficient strength without timbers by the use of thick laminatedf strings, the steps and risers to be well housed 
into both strings. Iron screws only should be used—no nails. 


* See Plate 45. 


f Sec Plate 8, Fig. 5. 








P L AT E N 0 . 7 . 



Fin 4 



4 




































































































































































































PLATE 8. 


Figs. I and 2. Bending Wood by Saw-kerfing. —This method of bending is the weakest 
practised, but owing to the fact that it is thought to be least expensive is frequently adopted, lo find 
the correct distance between saw-kerfs for any required radius of curvature, select a piece of stuff of 
suitable length and equal to the thickness of the material to be bent, as at Fig. i. Let A B equal 
the thickness of stuff, and A C the radius of the required curve ; make a saw-kerf at B 0 , leaving 
a thin veneer A 0 uncut, nail the cut piece at S K, and move it from C to D, or just enough to close 
the saw-kerf at B ; then C D being the distance moved will also be the exact space between each saw- 
kerf. The same gaged thickness of veneer A 0 must be kept, and the same saw used for the work to 
be done, as were used in the trial at Fig. i. 

Fig. 2. The Construction of a Circular Form Over Which the Saw-kerfed Material 
as Above Explained is Shown, Bent in Position. —E F G is the plank rib (made of three pieces) 
of which two or more are required, according to the work to be done. H J L are the staves which are 
nailed to the ribs and so complete the circular form. N M is a veneer laid over the form first, upon 
which is bent and glued the prepared saw-kerfed material P Q R ; this must be left on the form until 
the glue is perfectly dry. The piece of saw-kerfed work P Q R, should be drawn tight to the veneer 

and the form by means of hand-screws, as given by one example, T U, with curved blocks, V W. 

Fig. 3. Bending Wood and Keying.— This form is in plan the same as Fig. 2, except that 

the rib E F G is not curved at its lower edge ;—shaping the lower edge this way is done for the con¬ 

venient use of hand-screws in the manner shown at Fig. 2. 

By this method of bending, the wood is removed from the back of the stuff, as at XXX, etc., leaving 

the thickness of a veneer at the face ; then after bending, the grooves XXX are filled with tightly fitted 

strips of wood (glued in) called keys, as at S S S, etc. It greatly adds to the strength of this bent keyed 

work to glue on three strips of veneer,—one at each edge of the keyed stuff, and one in the middle. 

The glue should be perfectly dry before the work is removed from the form. The spaces between the 
keys may be determined by the same method as that used to find the spaces between saw-kerfs. 

Fig. 4. Bending a Veneer Facing and Filling out the Thickness with Staves. —The 
wood is removed wholly from the back of the stuff between the. points required, leaving a veneer facing 
which is bent over the form, and then staves, Z Z Z, etc., are fitted and glued on, as shown in this drawing. 

Fig. 5. Laminated Work.— Bending several thicknesses of veneer together is defined as lamina¬ 
ted work. The whole of the veneers required should be heated and bent over the form together and 
secured in place ; then releasing and applying glue to one-half, put it back in position again, and pro¬ 
ceed with the other half in the same way, pressing and binding solidly the whole together and to the 
surface of the form. 

To ascertain what thickness of white pine will bear bending without injuring its elasticity^ 77 iultiply the 
radius of curvature in feet by the deci//ial .05 a/id the product will be the thick/iess i/i i/iches:—For exa 77 iple, 
77 iultiply a four feet radius of curvature by the deci/zial given^ —q'.o" X .05=.20, equal to two teiiths or 07 ie- 
fifth of an inch thickness, that would betid without fracture. 

Fig. 6. Bending Stair-strings.— This drawing shows the construction of an ordinary quarter 
circle form with the correct position of a stair-string bent over it ; the ribs of this form are quarter 
circles and are set parallel to each other and at right angles to the chord line R P. 

Figs. 7 and 8. Construction of a Form for Bending Quarter Circle Stair-strings, the 
Ribs to be Set on an Angle Parallel to the Inclination of Such Strings. —There are two 
advantages claimed for forms built in this way ; one is, a saving of stuff ; the other, that the form 
occupies less room. 

Fig. 8 .—Plan of a quarter turn of winders with a circular wall-string. D E, the circular wall¬ 
string as laid out from the plan A B. At Fig. 7, L M and F FI is the position of the ribs parallel to 

D E the inclination of the circular string ; F G equals C A of Fig. 8—less the thickness of stave—and 

is the semi-minor axis, and F FI becomes the semi-major axis of an ellipse ; as the shape of the rib 
when placed on the oblique line F H, becomes a quarter ellipse. The ribs have to be beveled on the 
^edge to range with the lines L F and M FI, as shown. 

Figs. 9 and 10. Soffit Mouldings.— These mouldings, placed at the lower edge of stair- 
strings, have to be carried around cylinders, and this work can be done in different ways. A cylinder 
may be made of sufficient length and reinforced—filled out by gluing on pieces, as at 0 R S, Fig. 10— 
then the moulding is worked out solidly in connection with the cylinder. Another way is to shape up 
the lower edge of the cylinder filled out as at 0 R S, then fit and shape two or more solid pieces— 

depending on the size of cylinder—of a thickness and width sufficient to carry out a moulding similar 

to N P, Fig. 9. 

Figs. II and 12. To Find the Lengths of Cylinder Staves that Include Winder-treads. 

—Set up an elevation of treads and risers sufficient to get the shape of cylinder in its connections with 
the straight string and facia, as here shown and as before fully explained at Fig. 3, Pl.\te No. 4. Divide the 
opening out of the cylinder V W, into three equal parts, V Z, Z X and X W ; parallel to the risers draw 
the lines Z L, X S and W T ; then the length of each stave and its position is given at M B, L F 
and S X. The construction of this cylinder and the winder-treads contained in it are given at Fig. ii. 
The manner of splicing and connecting a staved cylinder with a straight string is given at Plate No. 3, 
Fig. 3. 


P LATE No. 8 . 




























































































































PLATE 9. 


The method of one-plane projection is where the projection on the horizontal plane is alone required. 
Merely illustrative examples are here given of the practical application of the 07 ie-plane method tn drawing face- 
moulds for hand-railing. 

Fig. I. To Find the Angle of Tangents and Centre Line Over a Plan of a 
Quarter-circle, where the Tangents are required to have a Common Inclination.— Let 

A V Y be the plan, with the tangents A U and U Y ; let A W U and U T Y be the common angles of inclination ; 
connect U X, the level line common to both planes; through Y and A draw the line R S indefinitely ; on U as 
centre with U T as radius describe the arc T S and the arc at R ; connect R U and S U ; bend a flexible 
strip and mark a curve through the points R V S: then R U S will be the length and angle of the tangents, 
and R V S the curve-line over the plan A V Y. To find the angle with ivhich to square the wreath-piece at both 
joints: —On U as centre describe the arc Z B ; connect B A : then the bevel at B will contain the angle 
sought. 

Fig. 2. To Find the Angle of Tangents and the Centre Line Over a Plan of a Quarter- 
circle when the Tangents have Different Inclinations.—Let the plan be A F M, with the tangents 
A B and B M ; let the two inclinations be A G B and b C M. To find the level line common to both planes : Make 
C Q equal to B G ; parallel to M B draw Q 0 ; parallel to M C draw 0 N; connect N K : then N K is the line 
sought. Parallel to N K draw B I ; at right angles to N K draw M D and A E; on B as centre with B C as 
radius describe the arc C D ; again, on B as centre with A G as radius describe an arc at E ; connect E B 
and B D ; bend a flexible strip and mark a curve through E F D ; connect E D : then E B D will be the 
lengths and angle of tangents, and E F D the curve-line over the plan A F M. To find the angle with which 
to square the wreath-piece at joint D ; Continue B M to L; make M L equal Q P ; connect L K : then the bevel 
at L contains the angle required. To find the angle with which to square the wreath-piece at the joint E : Draw 
I J parallel to M K; make I J equal B H ; connect J A: then the bevel at J contains the angle sought. 

Fig. 3. Plan of Hand-rail a Quarter-circle, with the Tangents to the Centre Line 
A F and F D, the Tangents to have Common Angles of Inclination. —Let A G F and F E D be 
the angles of a common inclination ; connect F X ; from K, parallel to F X, draw K L ; from J, parallel to 
D E, draw J M ; through A and D draw AC; on F as centre with F E as radius describe the arc E C. To 
find the angle with zvhich to square the wreath-piece at both joints : Make F H equal F I ; connect H A : then the 
bevel at H contains the angle sought. 

Fig. 4. To Draw the Face-mould from Plan Fig. 3.—Make B C, B C equal B C of Fig. 3 ; 
make B F at right angles to B C and equal to B F of Fig. 3 ; connect F C and F C ; make F M and F M each 
equal F M of Fig. 3 ; through M and M, parallel to B F, draw K L and K L ; make M L, M K, at each side of 
the centre equal J L and J K of Fig. 3 ; make B N 0 equal the same at Fig. 3 ; through C and C draw K P 
and K Q ; make C P equal C K, and C Q equal C K ; let C S equal straight wood, as required ; parallel to 
C S draw K T and Q R ; parallel to M C draw K U ; make the joints at right angles to the tangents ; 
through Q L 0 L P of the convex and K N K of the concave trace the curved edges of the face-mould. 

Fig. 5. Plan of Hand-rail a Quarter-circle, with Tangents to the Centre Line, Q Z and 
Z X, the Tangents to have Different Inclinations.—Let Q M Z and Z G X be the required inclina¬ 
tions of the tangents. To find a level line common to both planes : Make G H equal Z M ; draw H E parallel 
to Z X, and E V parallel to G X ; connect T P : then T P is the line sought. Parallel to T P draw I J, Z A and 
C D ; parallel to Z M draw R L ; parallel to X G draw Y F ; at right angles to P T draw X W and Q 0 ; on 

Z as centre with Z G as radius describe the arc G W ; again, on Z as centre with Q M as radius describe an 

arc at 0 ; connect 0 W. To find the angle with which to square the wreath-piece at joint 0 : Draw A B parallel 
to Q Z ; make A B equal Z N ; connect B Q : then the bevel at B contains the angle required. To find the 
angle with which to square the wreath-piece at joint W : Prolong Z X to K ; make Z K equal H 2 ; connect K P : 
then the bevel at K will be the angle sought. 

Fig. 6. Face-mould from Plan Fig. 3.—Make 0 U W equal the same at Fig. 5 ; on U as centre 
with U Z of Fig. 5 as radius describe an arc at M ; on 0 as centre with Q M of Fig. 5 as radius intersect 
the arc at M ; connect 0 M, M W and M U ; make M E F equal Z E F of Fig. 5 ; make M L equal M L of 
Fig. 5 ; parallel to M U draw I F J, 3 E V and C L D ; make L D, L C and M S 4 equal R D, R C and Z S 4 

of Fig. 5 ; make E V, E 3 and F J, F I equal T V, T 3, Y J and Y 1 of Fig. 5 ; through W draw I P ; make 

W P equal I W ; through 0 draw C R ; make 0 R equal 0 C ; make 0 T straight wood, as required ; parallel 
to 0 T draw C N and R Q ; make the joints at right angles to the tangent; parallel to W M draw I Z ; 
through R D S V J P of the convex and C 4 3 I of the concave trace the curved edges of the face-mould. 

Face-moulds, their Number and Character. 


1. Plan : Quarter-circle—one tangent inclined, the other horizontal. 

2. “ “ tangents “ alike. 

3. “ “ “ “ differently. 

4. Less than a quarter-circle—one tangent inclined, the other 

horizontal. 

5. “ “ More than a quarter-circle—one tangent inclined, the other 

horizontal. 


6. Plan : Less than a quarter-circle—tangents inclined alike. 

7- “ “ “ “ " differently in¬ 

clined. 

8. “ Elliptic or eccentric—tangents inclined alike, 

9. “ “ “ “ ’* differently. 

10. “ Greater than a quarter-circle—tangents inclined alike. 

11. “ “ “ “ “ “ differently. 


It is believed that the above list of eleven face-moulds comprises all that are required in hand-railing. 
There are two face-moulds, however, that are given in this work not on the list, one at Plate No. 34 and 
another at Plate No. 35, each of which include the whole cylinder—a semicircle. These may be called 
compound face-moulds, for the first is explained at Plate No. 14 and used at Plate No. 34, with a portion 
of the curve more than the face-mould proper, and worked with the wreath, thereby completing the semi¬ 
circle in one wreath-piece ; the other is double the face-mould given at Plate No. 10, the two used as 
one and worked as directed at Plate No. 35, completing the semicircle in one wreath-piece. 


Note.—T hese face-moulds are all given in the above order, beginning at Plate No. lo. 





PLATE N o. 9 . 



F 










































PLATE 10. 


•This plate is the first of ten prepared for the purpose of giving instruction in a simple and practical way 
in the scientific requirements of hand-railing, based on a few and easily-applied laws of geometry. 

The object and use of the solids—rectangular, acute and obtuse angled prisms—introduced in these ele¬ 
mentary plates, may be summed up briefly : as a convenient and direct means of imparting to workmen this 
branch of geometrical knowledge ; as demonstrating the importance and use of tangents as applied to hand-rail¬ 
ing, for two of the vertical sides of every prism given are tangent to a curve described on the base, and tangent 
to its trace on the cutting plane. The upper end of each prism is cut inclined on one or two angles of inclina¬ 
tion in the same plane, and shows the actual relation of the inclined or cutting plane to the horizontal plane or 
base ; * or, as maybe again stated, exhibits in every case the exact relation of a plan as given on the base and a 
section of the plan traced vertically on the inclined plane. The cutting plane, as produced on one end of these 
solids, is in each particular case the position of the plane or surface of plank out of which the wreath-piece 
has to be worked. The face-mould and its tangents are found on this plane ; therefore the face-mould when 
applied to the plank gives the shape of the convex and concave sides of the wreath-piece, which must hang 
vertically—or plumb—over the curved plan beneath. The paper representations of solids f are to be pre¬ 
ferred because they can be more easily and conveniently made than wood solids ; and in making them they 
afford instruction in detail that wood solids do not, because in the formation of solids with paper the surfaces, 
angles and curves all have to be found in their proper relation on one plane, which it will be seen is the 
practice and knowledge required for drawing face-moulds correctly. 

Fig. I. Represents a Solid Block or Prism Standing Vertically on a Square Base, 
A B D C, the Upper End Cut on an Inclined Plane, A E F C, forming Oblique Angles with the 
Sides A C and B D, and at Right Angles to the Sides ABE and C D F.—Upon the base is described 
a quarter-circle, B C, tangent to the sides of the solid C D and D B. As E F is parallel to the square base 
C A B D, it is therefore a level line on the cutting plane C A E f ; and as B D at the base and E F on the cut¬ 
ting plane are level lines, any measurement taken on level lines at the base, as G H, J K and L M, and carried 
vertically to the cutting plane, as G R, J P and L N, and then parallel to the level line F E set off as at R S, 
P Q and N 0 , will give trace points of a curve on the cutting plane perpendicularly over the plan curve at the 
base. 

Fig. 2. Construction of a Paper Representation of a Solid with its Angles, Surfaces 
and Curved Lines as Given in Perspective and Described at Fig. i.—Let A B C D be the square 
base of the solid, and D F C the angle of inclination over the base C D and A B ; make D V, B W and B E each 
equal D F and at right angles to the sides of the base ; connect E A, B W, W V and V D ; continue D C to T, 
and B A to U ; let A U equal A E, and C T equal C F ; connect U T. On A as centre describe the quarter- 
circle B C, tangent to the sides of the base C D and B D ; through any points on the curve H K M, parallel to 
the level line B D, draw the lines H G X, K J X and M L X ; make C N P R T equal C X X X F ; draw R S, P Q 
and N 0 parallel to U T, and equal to L. M, J K and G H : then U S Q 0 C will be the trace of a curve on the 
cutting plane lying perpendicularly over the plan curve B H K M C. With a sharp-pointed instrument scratch 
the lines A B, B D, D C and C A ; cut out the remainder of the figure and touch the adjoining edges with a 
little glue or thick mucilage and bring them together, leaving all lines on the outside, so that their connections 
may be seen and understood. 

Fig. 3. Plan of Hand-rail a Quarter-circle, with One Tangent to be Inclined, the 
Other Level. —B D and D C are the plan tangents to the centre line B C ; let D F C be the angle of inclina¬ 
tion over the plan tangent C D ; the tangent D B to remain level; parallel to D B draw E Q 0 , J MO and 
R S 0 . The bevel at F contains the angle with which to square the wreath-piece at joint B ; joint C is 
squared from the face of the plank. 

Fig. 4. Face-mould from Plan Fig. 3. —Make B F and F C at right angles ; let F C equal F C of Fig. 
3, and F B equal D B of Fig. 3 ; through B draw V E at right angles to B F; make B V equal B E ; make F 0 0 0 
equal F 0 0 0 of Fig. 3 ; parallel to F B draw 0 Z, 0 Y E, 0 X W and C G H ; make F I equal D U of Fig. 3 ; 
make 0 Z equal T S of Fig. 3 ; make 0 Y equal P N and P E of Fig. 3, and 0 X and 0 W equal L K and L J 
of Fig. 3, and C G and C H equal C G and C H of Fig. 3 ; through the points V I Z Y X G of the convex and 
E W H of the concave trace the curved edges of the face-mould. 

Fig. 5. Parallel Pattern for Round Rail, or to be Used Instead of the Face-mould for 
Marking the Wreath-piece on the Rough Plank. —The measurements are taken from the plan at 
Fig. 3, as indicated by the corresponding letters. Through the central points C M Q R B describe circles of 
any radius required ; touching these circles on the convex and concave bend a flexible strip of wood and 
mark the curved edges of the pattern. 

For ordinary-sized hand-rail wreath-pieces may be worked out of stuff as thick as the width of rail, and a 
parallel pattern about wider than the required width of rail. See Plate No. 56, Figs. 6 and 7. 


* It 5-houlcl be understood that the bases of all these solids are cut square, or at right angles to their length ; also at the upper 
end two adjoining sides of any solid may be cut on two different angles of inclination, or a common angle of inclination ; or one side 
may be cut at right angles to its length and the adjoining side at any inclined angle ; but in every case the opposite sides must be cut 
paraliel. f Drawing-paper, such as Whatman’s, is best to make paper representations of solids—pasteboard is too thick and clumsy. 




F 





F 1 G. 3 . 
































































PLATE 11. 


Fig. I. Represents a Solid Block or Prism Standing Vertically on a Square Base, 
ZXWY, the Upper End Cut on the Side Z X on the Angle of Inclination, XVZ, and on the 
Side X W on the Same Angle, K U V.—On the horizontal plane or base, Z Q W represents the plan of a 
quarter-circle to which the sides of the solid Z X and X W represent plan tangents ; also the lines Z V and V U 
represent the tangents on the cutting plane. The sides of this solid being cut on a common angle of inclina¬ 
tion, the heights from the base X and Y to X V and YT are alike, and therefore a line drawn on the cutting 
plane from V to T will be a level line ; and at the base a line drawn from X to Y will be a level line common 
to both planes. At any points on the curve at the base parallel to the level line X Y, draw 0 H and PN ; 
parallel to X V draw H R and N L ; parallel to VT draw L M and R S ; make L M equal N P, and R S equal 
H 0 ; make V J equal X Q; then the curve Z S J M U will lie perpendicularly over the plan-curve at the 
base Z 0 Q P W. 

Fig. 2. Construction of a Paper Representation of a Solid with its Curved Lines and 
Angles as Given in Perspective and Explained at Fig. i.—L et Y W X Z be the square base of the 
solid ; on Y as centre describe the quarter-circle W Q Z ; prolong X W both ways to C and V, Z X to E, W Y to 
3, and F and Y to B. Let X V Z be the angle of inclination over X Z ; make Z X E, W K and K F each equal 
X V ; connect K E and F E ; then K F E will be the same angle of inclination over W X as X V Z is over X Z ; 
make W D, D C, Y B and Y 3 each equal X V ; connect C B and 3 Z. Through Z W draw A A ; on Z as centre 
with A A for radius describe an arc at U ; on V as centre with V Z as radius intersect the arc at U ; and again 
on Z as centre with Z 3 for radius describe an arc at T; and on V as centre with X Y for radius intersect the 
arc at T ; connect Z T, T U, V U and V T ; at right angles to Z T draw T 2 ; from K draw K 1 at right angles 
to E F ; at any points on the plan-curve draw P N and 0 H parallel to Y X ; draw N G parallel to W F, 
and H R parallel to X V ; draw R S and L M parallel to V T ; make L M, V J and R S equal H 0 , X Q and N P ; 
through Z S J M U trace a curve that will lie perpendicularly over the plan-curve W P Q 0 Z. 

With a sharp-pointed instrument scratch the lines A B, B C, C D, DA and H A ; cut out the remainder of 
the figure and touch the adjoining edges with a little glue or thick mucilage and bring them together, leaving 
all lines on the outside, so that their connections may be seen and understood. 

Fig. 3. Plan of Hand-rail a Quarter-circle, the Plan-tangents Z X and W X to Have the 
Common Angle of Inclination, XVZ and WFX. Through WZ draw A A with X F as radius; on X as 
centre with X F as radius describe the arc F A and A : then A A will be the distance on the cutting plane over 
W and Z ; and if lines be drawn from A to X and A X, then A X and A X will be the length and angle of tangents 
on the cutting plane. From B, parallel to X Y, draw B J ; from N, parallel to W F, draw N M. To find the 
angle for squaring the wreath-piece at both joints : Make X E equal X G ; connect E Z : then the bevel at E 
will give the angle sought. By reference to Fig. 2 when put together as a solid it will be seen that the line 
T 2, which is parallel to the joint required at U, is on the inclination of the cutting plane—or face of plank—in 
that direction, and with the line I K—which is on the vertical plane—will be the angle of a plumb-line on the 
butt joint of such a wreath-piece as this centre line Z U applies to. 2 T of Fig. 2 equals Z E of Fig. 3 ; K I 
equals X G E of Fig. 3, and the angle T 2, I K of Fig. 2 equals the angle Z E X of Fig. 3. 

Fig. 4 Face-mould over a Quarter-circle, the Tangents of a Common Inclination, as 
Given and Explained at the Plan Fig. 3.—On a line FZ make K Z and K F each equal A K of Fig. 3 ; 
make K V at right angles to Z F, and equal to K X of Fig. 3 ; connect Z V and F V ; make F N and Z H each 
equal F M of Fig. 3 ; through H and N draw T D and J B, at right angles to F X ; make V S K equal X S K of 
Fig. 3 ; make H T and H D, and N J and N B each equal N J and N B of Fig. 3. Through F draw B I ; make 
F I equal F B ; through Z draw D I ; made Z I equal Z D ; through I T S J I on the convex, and D K B on the 
concave, trace the curved edges of the face-mould. The joints Z and F are made at right angles to the 
tangents. The slide-line will be explained further along. 

Fig. 5. Parallel Pattern for Round Rail, or to be Used Instead of the Face-mould (as 
a Means of Saving Stuff) for Marking the Wreath-piece on the Rough Plank. —On the line 
A A make K A, K A each equal K A of Fig. 3 ; at right angles to A A draw K X, equal to K X of Fig. 3 ; connect 
X A, X A and make the joints A, A at right angles to A X ; make A N, A N each equal F M of Fig. 3 ; make N P, 
N P each at right angles to A A, and equal to N P of Fig. 3 ; make X Q equal X Q of Fig. 3. describe circles 
on the centres A P Q P A of any required radius for width of pattern. For ordinary-sized hand-rails—stick as 
2" thick by 3” wide, 2]^" thick by 3^” wide, 2^" thick by 4” wide—any wreath-piece may be worked out of stuff as 
thick as the width of hand-rail, tvith a parallel pattern like Fig. 5 about wider than the width of the 
hand-rail. See Plate No. 56', Figs. 6 and 7. 

Fig. 6. Exhibits the two Solids Presented—that of Fig. i, Plate No. 10, and Fig. i. 
of This Plate—brought together, the quarter-circle of each completing the plan of a semicircle on the 
horizontal plane and showing the vertical trace of the semicircle on the cutting planes of the two differently- 
cut solids. 

Fig. 7. This Solid is Reproduced Half the Size of Fig. i, merely to be Used for the 
Purpose of Showing the Correctness of A A and the Angles A A X, as Described at Fig. 3.— 

In this figure V T, as before explained, is a level line on the cutting plane, and X Y the position of a level line 
on the horizontal plane common to both planes. Now if a vertical plane be conceived with Z W as base, it 
would touch F and Z on the cutting plane, and F Z on that plane would be the distance required in position 
on the horizontal plane. Extend the base of the vertical plane W Z to A A indefinitely. On the horizontal 
plane, X being vertically under V of the cutting plane, and V I and X K measuring alike on both planes, set one 
foot of the compasses on X, and with Z V or V F for radiu-s de.scribe arcs at A A : then A X A and their angles 
on the horizontal plane will equal the angles Z V F on the cutting plane. 




P LATE N 0. 1T . 



F I G . 5 . 



F I G . 4 



F I G. 6 





































































































































PLATE 12. 

Fig'. I. Represents a Solid Block or Prism Standing Vertically on a Square Base 
A B C D, the Upper End Cut on an Inclined Plane Containing the Two Different Inclina¬ 
tions A E B and t G F.—Let A N C represent a quarter-circle to which the sides of the solids A B and B C 

are tangent, T’o find the direction of a level line on the cutting plane from the point H : make C I equal D 
H, connect H I ; draw I J parallel to the base C B : then J H will be the level line sought. Draw J M parallel 
to E B: then M D on the horizontal plane will be the direction of a level line common to both planes; again, 
from the point E, a level line E 0 will be found by making D Q and T 0 equal to B E ; then B T on the hori¬ 
zontal plane will be the direction of a level line as before. These level lines T B, 0 E, D M and J H, being 
all of the same length, so all level lines drawn on the base to which perpendicular lines and level lines on the 
cutting plane are drawn, and equal measurements taken from the curve at the base (as B N and E P), will 
give the trace of the curve on the cutting plane perpendicularly over that at the base. As the sides of the 
solid A B and B C at the base, are tangent to the curve, so A E and E G are tangent to the curve traced on the cut¬ 
ting plane. A level line co/nnion to both planes may be demonstrated as follotvs : prolong the inclination G H until 
it meets the prolongation of the horizontal plane C D c?/ R ; also continue the inclination G E until it meets the con¬ 
tinuation of the base C B S ; connect S' R : then S R is the intersecting line of the plane of the two inclinations G E 
and E A, and the horizontal plane C R and C S ; also S R is the position of a' level line common to both planes. 

Fig. 2. Construction of a Paper Representation of the Solid with Its Curved Lines 
and Angles as Given in Perspective and Described in Fig. i.—Let A B C D be the square base . 
of the solid ; on D as centre describe the quarter-circle A U V C. Prolong B C both ways to Z and N ; D C 

to Y and I ; A D to P and A B to M. Let B Z A be the inclination of the plan tangent B A ; make B M and C K each 

equal B Z ; let K I M be the inclination of the plan tangent C B ; let C 0 , D P and D Y each equal K I ; make 0 N 
equal B Z ; connect N P and Y A. To find the direction of a level line on the horizontal plane from the point B, 
make D 2 equal B Z, draw 2 3 at right angles to Y D ; and 3 X parallel to Y D : then X B will be the direction of the 
line sought ; to find the level line from the point D, make C J equal D Y, and draw J L parallel to C B ; from L 
draw L W parallel to C I : then D W will be the direction of a level line common to both planes from the 
point D. From A and C at right angles to the level lines X B or W D, draw A G and C H indefinitely ; with 

Z A as radius on B as centre describe an arc at G, and with M I as radius on B describe an arc at H : then 

H G will be the distance on the cutting plane over C-A of the plan, and if lines are drawn from H to B, and 
from G to B, the lengths and angle of tangents on the cutting plane will be given. With M I as radius set 
one leg of the compasses on X and describe an arc at E, and with H G as radius, on A intersect the arc at E, 
connect Z E, make Z T equal M L ; on A with A Y as radius describe the arc Y F ; with Z A as radius on E 

intersect the arc at F ; connect E F and F A ; connect F T ; on A describe the arc 3 Q ; connect Q Z ; make 

Z R equal B U, and T S equal W V : then the curve ARSE will be the trace on the cutting plane perpen¬ 
dicularly over the curve at the base. From F at right angles to A F draw the line F 4, and from F at right 
angles to F E draw F 6 ; from P at right angles to P N draw P 8 ; from J at right angles to I M draw J 5. 
With a sharp-pointed instrument scratch the lines A B C D, and Z A ; then with a sharp knife cut through the 
outlines of the figure, and touch the adjoining edges with a little glue or thick mucilage and bring them 
together, leaving all lines on the outside for examination. 

Fig. 3. Plan of Hand-Rail a Quarter-Circle in which the Tangents to the Centre 
Line C B and A B Require Two Different Inclinations as B E C and A S B.—The plan of rail in 
every case consists simply of the convex and concave curve lines embracing the width of the rail, also the 
centre curve line and its tangents ; there has then to be added to this plan certain lines, which in their posi¬ 
tion fix the kind of face-mould required, and supply points of measurement from which to draw the face- 
mould. Let the inclination of the tangents B E C and A S B be first fixed, then find the direction of a level 
line common to both planes as follows : Make B F equal A S ; draw F J parallel to B C ; from J draw J I 
parallel to E B ; connect 1 D : then I D will be the level line sought. Parallel to D 1 draw L 6, R B and P X ; 
from 8 parallel to B E draw 8 W ; from V parallel to A S draw V U. To find the distance over C A on the cut¬ 
ting plane ; from C and from A, at right angles to I D, draw C H and A G indefinitely ; with C E as radius 

set one foot of the compasses on B and describe the arc at H, and with B S as radius on B describe the arc 
S G ; connect G H ; then G H will be the distance sought ; and if B H and B G are connected the lines will 
contain the angle and length of tangents on the cutting plane. To find the angles with which to square the 
wreath-piece : prolong B C to Z ; make C Z equal I K; connect Z D : then the bevels at Z will give the plumb 
line to square the wreath-piece at the butt-joint over C. Continue B A to Q ; make A Q equal A T ; connect 
Q R : then the bevel at Q will give the plumb line to square the wreath-piece at the butt-joint over A. 

Fig. 4. Face-mould Over a Plan of a Quarter-circle, the Tangents of Two Different 
Inclinations as Given at Fig. 3.—Draw the line C A and make C 0 and 0 A equal H 0 and 0 G of Fig. 3, 

On C with the radius C E of Fig. 3 describe an arc at E ; on 0 with the radius 0 B of Fig. 3 describe an 

intersecting arc at E, and on A with the radius B S of Fig. 3 intersect the arc at E ; connect C E, A E and 0 E; 

make C, 8, I equal C W J of Fig. 3 ; make E V equal B U of Fig. 3. Parallel to 0 E through 8, I, V draw 

L 6, M Y and P X; make 8, 6, 8 L, I Y, I M, E 4 N and V X and V P each equal the corresponding letters of 

Fig. 3. Through C draw L B ; make C B equal C L ; through A draw P D ; make A D equal A P. Through 

L M N P on the concave, and B 6 Y 4 X D on the convex, trace the curves of the face-mould. The joints A 
and C are made at right angles to the tangents A E and C E. The slide line is drawn anywhere on the face- 
mould at right angles to the level line 0 E. 

Fig. 5. Parallel Pattern for Round-rail or to be Used Instead of the Face-mould—as 
a Means of Saving Stuff—for Marking the Wreath-piece on the rough Plank.—Make H O 
and 0 G each equal H 0 and 0 G of Fig. 3. The tangents H B and G B, and the level line B 0 , are the 
same as Fig. 4. Make H I and B V equal C J and B U of Fig. 3 ; draw 1 , 5 and V 2 parallel to 0 B ; make 
V 2, B 3 and I, 5 each equal the corresponding letters and figures at Fig. 3. The joints are made at right 
angles to the tangents. Describe circles an the centres H 5, 3, 2 G, of any required radius for width of 
pattern. Fig. 6 .—A solid similar to Fig. i introduced to call attention to the two sections that may be cut in a 
direction on the inclined plane, at right angles to each of the differently inclined sides or tangents, rt'j' A B and B C ; 
and also cut down the sides of the solid in a direction at right angles to each inclination of the cutting plane <75 A D 
and C E. The inclined plane of these solids should be understood as representing the surface and position of rail 
plank ; the lines A B and B C the direction of joints of face-moulds ; and the lines A D and C E represent the joints 
square through the thickness of plank. The angle BCE will square the wreath-piece at the butt-joint F G ; and 
the angle BAD squares the wreath at the joint H I. The sections here given and described are also outlined on the 
paper solid to be formed at Fig. 2 by the lines F 7, 7, 6 and P 8, also F 4 and J 5. 





P LATE N 0. 1 2 



E 



F I G. 3 . 








































































































PLATE 13. 


V Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base A B P 0 , 

the Sides of Which are Parallel, and Have Two Obtuse and Two Acute Angles. —The 
upper end of this prism is cut on the inclination P M B, and M N at right angles to the sides, and parallel to 
the base P 0 . In this solid B A, being in the horizontal plane, and also terminating the inclined plane, is a 
level line common to both planes. On the base describe the curve A D J P tangent to the sides of the solid 
A B and BP. To find the trace of this plan curve on the cutting plane : parallel to A B on the base and at 
pleasure draw C D and G J ; at G and C parallel to P M draw G K and C E ; from E and K parallel to B A 
draw K L and E F ; make E F equal C D, and K L equal G J ; through the points A F L M on the inclined 
plane trace a curve perpendicularly over the plan curve A D J P, As the sides of the solid A B and B P at 
the base are tangent to the plan curve, so A B and B M are tangent to the curve traced on the cutting plane. 

Fig. 2. Construction of a Paper Representation of the Solid With its Curved Lines 
and Angles Given in Perspective and Described at Fig. i.—Let A B P 0 be the form of the 
base, the opposite sides of which are parallel and equal. From A at right angles to B A draw A X ; from P at 
right angles to B P draw R X ; on X as centre describe the plan of curve A D J P, tangent to the sides of the 
base B A and B P. Let P R B be the inclination—assumed or required—over the base B P ; make 0 N and 
P M at right angles to 0 P and each equal P R ; connect N M ; make 0 U at right angles to A 0 and equal 
to P R ; connect U A ; parallel to B A from any points on the curve D and J draw J G and D C ; parallel to 
P R draw C E and G K ; on B with B R as radius describe the arc Q R S indefinitely ; on A with A Q as 
radius intersect the arc at S ; connect SB; on A with A U as radius describe an arc at T ; on S with B A as 
radius intersect the arc at T ; connect A T and T S. On B as centre describe the arcs K W and E V ; draw 
V F and W L parallel to B A ; make V F and W L equal C D and. G J ; through S L F A trace a curve on the 
cutting plane that will lie perpendicularly over the plan curve A D J P. With a sharp-pointed instrument 
scratch the lines A B P 0 A ; cut out the remainder of the figure and touch the adjoining edges with a little 
glue or thick mucilage and bring them together, leaving all lines on the outside for examination and study. 

Fig. 3. Plan of Hand-rail Less than a Quarter-circle, the Tangents to the Centre 
Curve Line A P Forming the Obtuse Angle P B A.—From P draw P M and P 5 at right angles to 
B P ; draw A 5 at right angles to B A ; on 5 as centre describe the curve A P. The position of the tangent 
A B is horizontal, while over the tangent B P the inclination P M B is required. Draw T 0 , R L, U G and X C 
parallel to B A ; parallel to P M draw J K, F I E, S N and 0 Q ; from P at right angles to B A draw P 4 ; on 
B with B M as radius describe the arc M 4 : then 4 A will be the distance over A and P on the cutting plane, and 
if a line be draiun from 4 to B, then 4 B A ivill be the length and angle of tangents ofi the cutting pla 7 ie. To find 
the angle for squaring the wreath-piece at the joint over P : draw E Z parallel to B P ; from F parallel to 
B M draw F H ; draw X Y at right angles to P M ; make X Y equal P H ; connect Y Z : then the bevel at Y 
will give a plumb-line on the butt-joint over P, which is the angle sought. To find the angle for squaring the 
wreath at the joint over A : make D C equal J K ; connect C A : then the bevel at C will give a plumb-line on 
the butt-joint and the angle sought. 

Fig. 4. Face-mould Over a Plan of Less than a Quarter-circle with One Tangent 
Fixed in the Horizontal Plane, the Other Inclined as Given at the Plan of Hand-rail, 
Fig. 3. —Make M W equal A 4 of Fig. 3 ; with B M of Fig. 3 as radius set one foot of the compasses on M 
and describe an arc at B ; on W, with A B of Fig. 3, intersect the arc at B ; connect W B and B M. Make 
the joints W and M at right angles to the tangents. Make M K I N equal M K I N of Fig. 3 ; through K 1 N 
parallel to W B draw C L, A J and E G ; make K G equal J X, and K E equal J W of Fig. 3 ; through M draw 
G F ; make M F equal G M ; make I J and I A equal F G and F U of Fig. 3 ; make N L and B 6 equal S L 
and B 6 of Fig. 3 ; make W D equal W C. Through G J L 6 D on the convex and F E A C of the concave 
trace the curved edges of the face-mould. 

Fig. 5. Parallel Pattern for Round-rail or to be Used Instead of the Face-mould as a 
Means of Saving Stuff, and for Marking the Wreath-piece on the Rough Plank. —Make 
A M equal A 4 of Fig. 3 ; make the tangents M B and B A equal M B and B A of Fig. 3 ; make M F 0 equal 
M 1 Q of Fig. 3 ; make F V and 0 T equal F V and O T of Fig. 3. The joints are at right angles to the tan¬ 
gents. On M V T and A, describe circles of any required radius for width of pattern. 


* Tangents to any plan curve that includes less than a quarter-circle, or a curve that measures less than ninety degrees, always 
form obtuse angles. 



















































































































































































































PLATE 14. 


Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base A B C D the 
Sides of which are Parallel and Have Two Acute and Two Obtuse Angles. —The upper end 
of this prism is cut on the inclination CEB, and on the line E G at right angles to the sides and parallel to 
the base C D. The base line B A of this solid, being in the horizontal plane and also terminating the inclined 
plane, is a level line common to both planes. On the base draw the lines A Y and C Y at right angles to the . 
tangents ; on Y as centre draw the plan curve A L H C. At Plate No. 13, Fig. i, the solid is precisely like 
thiSf but the obtuse angled tangents to the curve were required in that case, because tke plan curve was less than a 
quarter-circle ; here, however, the acute angle must be used because the plan curve is greater than a quarter-circle* 
At any points on the curve as L and H parallel to A B draw L O and H J ; parallel to C E draw 0 N and J K; 
from K and N parallel to A B draw N M and K F ; make N M equal 0 L and K F equal J H ; through the 
points A M F E trace a curve on the cutting plane, which will lie perpendicularly over the plan curve A L H C. 
As the sides of the solid A B and B C at the base are tangent to the plan curve, so A B and B E are tangent 
to the curve traced on the cutting plane. 

Fig. 2. Construction of a Paper Representation of the Solid with its Curved Lines, 
Surfaces and Angles as Given in Perspective and Described at Fig. i.—Let A B C D be the 
form of the base, the opposite sides of which are parallel and equal. Draw A Y and C Y at right angles to 
the tangents ; on Y as centre describe the plan curve A 0 L C. Let C E B be the inclination over the base 
C B ; make C H and D G at right angles to C D and equal to C E ; connect H G ; make D I at right angles 
to A D and equal to D G ; connect I A. On B with B E for radius describe the arc E F and the arc K ; on A 
as centre with A I as radius, describe an arc at J ; on A as centre with A F as radius intersect the arc at K ; 
with B A for radius on K intersect the arc at J ; connect A J, J K and K B. Parallel to A B from any point 
on the curve 0 and L draw 0 N and L M ; parallel to C E draw M P and N R ; make BUT equal B R P ; 
parallel to B A draw U Q and T S ; make U Q and T S equal N 0 and M L. Through K S Q A trace a curve 
on the cutting plane that will lie perpendicularly over the plan curve A 0 L C. With a sharp-pointed instru¬ 
ment scratch the lines A B, B C, C D and D A ; cut out the remainder of the figure and touch the adjoining 
edges with a little glue or thick mucilage and bring them together, leaving all lines on the outside for com¬ 
parison and study. 

Fig. 3. Plan of Hand-rail Greater Than a Quarter-circle, the Tangents to the Centre 
Curve Line A C Forming the Acute Angle A B C.—Draw C Y, C E at right angles to C B ; draw A Y 
at right angles to A B ; on Y as centre describe the centre curve line A N M C. The tangent A B is to remain 
level, and over the tangent B C the inclination C E B is required. Through I and T draw I R and T V 
parallel to A B ; at any point on the curve as X draw K G parallel to A B ; parallel to C E draw Q 0 , K L and 
V P. From C at right angles to A B draw C F indefinitely ; on B as centre with B E as radius describe the 
arc E F : then A F will be the distance over A and C on the cutting plane ; and if a line be drawn from F to B, 
then F B A ivill be the length and angle of tangents on the cutting plane. To find the angle for squaring the 
wreath-piece at the joint over C : From K draw K H parallel to B E ; make C S equal C H ; connect S J : 
then the bevel at S will give a plumb line on the butt-joint which is the angle sought. To find the angle for 
squaring the wreath-piece at the joint over A : make Z G equal K L ; connect G A : then the bevel at G will 
give a plumb line on the butt-joint over A and the angle sought. In finding angles for squaring wreath-pieces 
as much of the joint lines as are convenient may be taken, as follows : Prolong the joint line C Y until it meets the 
continuation of the level line B A 8, make C 6 equal C 5 ; connect 6, 8, and the same angle will be given at C, 6, 8 

C S J : and again at joint A ; from C draw the line C 7 parallel /(? B A ; prolong the joint line to 2 \ 
make 2, 7 equal C E : connect 7 A ; then the angle 2, 7 A equals the angle Z G A. 

Fig. 4. Face-mould Over a Plan of Hand-rail More Than a Quarter-circle, the Plan 
Tangents Forming an Acute Angle, One of the Tangents to Remain Level, the Other 
Inclined, as Given at the Plan Fig. 3. —Make A E equal A E of Fig. 3, with E B of Fig. 3 as radius ; 
set one foot of the compasses on E and describe an arc at B ; on A with A B of Fig. 3 as radius intersect the 
arc at B ; connect E B and A B ; make E 0 L P equal E 0 L P of Fig. 3. Parallel toA B draw P C, L D and 
0 F, 0 G ; make 0 G, 0 F equal Q I and Q R of Fig. 3 ; connect G E H ; make E H equal E G ; make L J D 
equal K 3 X of Fig. 3 ; make P K C equal V W T of Fig. 3 ; make B M equal B U of Fig. 3. The joints E 

and A are at right angles to the tangents. Make A N equal A C. Through the points H F J K M N on the 

convex and C D G of the concave trace the curved edges of the face-mould. 

Fig. 5. Parallel Pattern for Round-rail, or to be Used Instead of the Face-mould as 
a Means of Saving Stuff, and for Marking the Wreath-piece on the Rough Plank.— A E B 
equals A F B of Fig. 3 ; E L P equals E L P of Fig. 3 ; L M and P N equals K M and V N of Fig. 3. The 

joints are at right angles to the tangents. On E M N A as centres describe circles of any required radius for 

width of pattern. 


* Tangents to any plan curve that includes more than a quarter-circle, or that measures more than ninety degrees, always form 
acute angles. 




Plate No.14-. 
























































































































































PLATE 15. 


Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base A B C D, 
the Sides of Which are Equal and Parallel, and Have Two Acute and Tw;o Obtuse 
Angles. —The upper end of this prism is cut on the angle B F A on the side A B ; and on the side B C, on 
the same angle of inclination G H F ; therefore, the sides of this solid have a common inclination, and a line 
F I drawn on the cutting plane, or B D on the horizontal plane, is a level line common to both planes. On 
the base A 0 X M C represents a plan curve less than a quarter-circle, to-which the sides A B and B C of the 
solid represent the plan tangents ; and the lines A F and F H represent the tangents on the cutting plane. 
To find the trace of the plan curve on the cutting plane at any points, aSC) X M,* draw 0 J and N M parallel 
to D B ; parallel to B F draw J K and N Q ; parallel to F I draw Q P and K L ; make Q P equal N M and 
K L equal J 0 ; make F R equal B X ; through the points A L R P H trace a curve on the cutting plane which 
will lie perpendicularly over the plan curve A 0 X M C. 

Fig. 2. Construction of a Paper Representation of a Solid With its Surfaces Curved 
Lines and Angles as Given in Perspective and Described at Fig. i.—Let A B C D be the form 
of base the opposite sides of which are parallel and equal. Draw C X and A X at right angles to the tangents; 
on X as centre describe the plan curve A J C. At^ right angles to A B and C D draw B F, C V and D W ; at 
right angles to A D and B C draw D Y, C U and B E. Let B F A be the inclination required over the base— 
or plan tangents—A B and B C. Make B E, C 2, 2 U, C Z, Z V, D W and D Y all equal B F ; connect U E, 
V W and Y A. Through C and A draw S T indefinitely ; on B as centre with F A as radius describe arcs at 

S and T. At any points on the curve, as 1 and 5, draw I K and 5 M parallel to D B ; parallel to B E draw 

M N ; parallel to B F draw K L ; on A with S T as radius describe an arc at H ; on F as centre with D B the 
level line as radius describe an arc at I ; on F with F A as radius intersect the arc at H ; on A as centre with 
A F as radius intersect the arc at I ; connect A I, I H, H F and F I. Make F R equal E N ; parallel to F I 
draw R Q and L 0 ; make L 0 equal I K, F P equal B J,and R Q equal M 5 ; through A 0 P Q H trace 
a curve on the cutting plane that will lie perpendicularly over the plane curve A J C at the base. With a 
sharp-pointed instrument scratch the lines A B C D A and A F; cut out the remainder of the figure, and touch 
the adjoining edges with a little glue or thick mucilage and bring them together, leaving all lines on the out¬ 
side so that their connections may be seen and studied. 

Fig. 3. Plan of Hand-rail Less Than a Quarter-circle, the Tangents A B and B C to 
the Centre Curve Line A C, to Have a Common Angle of Inclination. —At right angles to B C 
draw C H, C R ; at right angles to A B draw A R ; connect R B ; then R B is the direction of a level line 

common to both planes ; let C H B be the inclination assumed or required over the tangent C B, and let 

B V A be the same angle of inclination over the tangent B A ; B V being at right angles to A B ; through E 
draw E G parallel to R B ; parallel to C H draw J K. Through A C draw the line b T indefinitely ; on B as 
centre with B H as radius describe the arc H T and S : then S T will be the distance over C and A on the 
cutting plane ; and if lines be drawn from T and S to B : then the lines T B and S B will be the length and 
angle of the tangents on the cutting plane. To find the angle for squaring the wreath-piece at both joints : con¬ 
tinue B C Y indefinitely ; make C Y equal C L ; connect Y R : then C Y R will be the angle required and the 
bevel at Y will give a plumb-line on the butt-joints of the wreath-piece over A and C. 

Fig. 4. Face-mould Over a Plan of Hand-rail Less Than a Quarter-circle, the Plan 
Tangents Forming an Obtuse Augle, and the Inclination of Both Tangents Alike, as Given 
at the Plan Fig 3. —Let S D and D f equal S D and D T of Fig. 3 ; draw D B at right angles to S T 
and equal to D B of Fig. 3 ; connect T B and S B. Make B X, B 0 equal B U, B Q of Fig. 3 ; make T J, 
S J each equal H K of Fig. 3 ; through J and J draw lines at right angles to S T or parallel to D B ; make 
J G and J E at both ends equal J G and J E of Fig. 3 ; through T draw E Z ; make T Z equal T E ; through 
S draw E Z ; make S Z equal S E. The joints S and T are at right angles to the tangents. Through 
Z G 0 G Z of the convex and E X E of the concave trace the curved edges of the face-mould. 


* As many level lines may be drawn on the plan curve for measuring trace points on the cutting plane, as for face-moulds as .teem 
desirable. But in drawing face-moulds, certain points on the plan must always be taken with the level measuring lines ; as, for in¬ 
stance, the angle of tangents B, and the points E, both of Fig. 3. 




Plate No. 15 . 





























































































PLATE 16. 

Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base A B C D 
the Sides of which are Equal and Parallel and have Two Acute and Two Obtuse 
Angles; the Upper End of the Solid is Shown as Cut on Two Different Angles: the 
Side A B on the Angle B M A, and the Side B C on the Lesser Angle V Q M.*—On the 
base A E G H C represents a plan curve less than a quarter-circle, to which the sides A B and 
B C of the solid represent the plan tangents, and the lines A M and M Q represent the 
tangents on the cutting plane. Make B L equal D S, draw LJ parallel to A B, connect J S; then 

J S will be a level line on the cutting plane. Make J F parallel to B M, connect FD; then FD 

will be the direction of level lines on the horizontal plane common to both planes. At any points 
on the curve at the base, as E G H. draw BG and I H parallel to F D; pariillel to B M draw 

I P; draw P 0 and M N parallel to J S; make P 0 equal I H, M N equal B G, and J K equal 

F E; through A K N 0 Q trace a curve on the cutting plane which will lie perpendicularly over 
the plan curve A E G C. 

Fig. 2. Construction of a Paper Representation of a Solid -with its Angles, Surfaces, 
and Curved Lines as Given in Perspective and Described at Fig. i. —Let A B C D be the 
form of base the opposite sides of which are parallel and equal. Draw A T and C T at right 

angles to the tangents; on T as centre describe the plan curve A 0 P R C. At right angles to 

A B and C D draw B H, C X. and D V; at right angles to B C and A D draw B G, C F, and D U; 

let B H A be the angle of inclination required over the base or plan tangent A B; make B G 

and C I each equal B H; connect G I; make I F G the angle of inclination over the base or plan 
tangent B C, IF to be less in height than B H; make D U, C W and D V eacli equal I F; connect U A; 
make W X equal B H: connect XV. Make B L equal D U; draw L M parallel to BA; make M N parallel 
to B H: then N D will be the direction of level lines common to both planes. At right angles to D N 
draw CZ and A Y indefinitely; on B as centre with A H for radius describe an arc at Y, and again on B 
as centre with G F for radius describe an arc at Z: then Y Z will be tne distance over A and C on the 
cutting plane, and if lines are drawn from Z to B and Y to B, then Z B and Y B will be the length 
and angle of the tangents on the cutting plane. From B parallel to N D draw B P, and at any 
point on the curve, as R, draw R Q parallel to N D. On R as centre with G F as radius describe 
an arc at K; on A as centre with Y Z as radius describe an arc at K; on A as centre with A U 
as radius describe an arc at J; on M with N D as radius intersect the arc at J; connect A J, J K 

and K H; make H E equal G 5 ; parallel to M J draw H 2 and E 4 ; make M S equal N 0 , H 2 

equal B P, and E 4 equal Q R, through A S 2 4 K trace a curve on the cutting plane that will 
lie perpendicularly over the plan curve A 0 P R C at the base. With a sharp-pointed instrument 

scratch the lines A B, B C, C D, DA and H A; cut out the remainder of the figure and touch 

the adjoining edges with a little glue or thick mucilage and bring them together, leaving all 
lines on the outside so that their connections may be seen and understood. 

Fig. 3. Plan of Hand-rail Less than a Quarter-circle, the Tangents to have Two 
Different Angles of Inclination, the Angle B F A over the Tangent A B, and C S B the 
Lesser Angle over the Tangent C B.—To find the position of a level line common to both 

planes: draw A L parallel and equal to B C; make B W equal C S; draw W X parallel to B A; 

make X U parallel to B T; connect U L: then U L will be the line sought. Parallel to U L 
draw P Q, B M and G H; parallel to C S draw 0 R; parallel to U X draw F 4 . At right angles 
to L U draw C D and A E indefinitely; on B as centre with B S as radius describe the arc S D, 
and again on B as centre with T A as radius describe an arc at E: then D E will be the distance 
over A and C on the cutting plane; and if lines are drawn from E and D to B, D B and E B 
will then be the length and angle of tangents on the cutting plane. 

To Find the Angle for Squaring the Wreath-piece at the Joint over C:—Prolong 
the tangent B C to N; make C N equal C R; connect N M: then the bevel at N will give a 
plumb-line on the butt-joint over C. 

To Find the Angle for Squaring the Wreath-piece at the Joint over A:—Prolong 
the level line U L until it meets the continuation of the joint-line A K at J; prolong the tangent 

BA to i; make A I equal U V; connect I J: then the bevel at 1 will give a plumb-line on the 

butt-joint over A. 

Fig, 4. Face-mould over a Plan of Hand-rail Less than a Quarter-circle, with Two 
Different Angles of Inclination over the Plan Tangents. —Let A H equal E D of Fig. 3. 
Make H Z equal D Z of Fig. 3. On Z as centre with Z B of Fig. 3 as radius describe an arc 
at B; on H as centre with S B of Fig. 3 as radius intersect the arc at B; connect H B and A B, 
and if the work is correct A B will equal A T of Fig. 3. Connect B Z; make H Q equal S R of 
Fig. 3; make A P and A R equal A 4 and A X of Fig. 3; through Q parallel to B Z draw K G, 
through R and P parallel to B Z draw M E and N D; make Q K and Q G equal 0 Q and 0 P 

of Fig. 3; make B F equal B 2 of Fig. 3; make R M and R E equal U Y and U 3 of Fig. 3; 

make P N and P D equal F H and F G of Fig. 3; through A draw D 0 ; make A 0 equal A D; 

through H draw G I; make H I equal H G; through I K M N 0 of the convex and G F E D of 

the concave trace the curved edges of the face-mould. The slide-line on a face-mould is always 
drawn at right angles to the level line. 


* The opposite sides of all the solids must be cut on parallel angles of inclination. 





PLATE No.16. 



Fig. 4 . 


k 



































































































PLATE 17. 

Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base of the 
Given Form A B C D, the Parallel Sides of which are Equal, but Two of the Sides are 
Larger than the Other Two. The Upper End of the Solid is Shown as Cut on Two 
Different Angles: the Side A B on the Angle of Inclination B J A, and the Side B C on the 
Angle of Inclination G F J.—On ilie base A Q P C represents a plan curve elliptic or eccentric, 
to which the sides of the solid A B and B C represent the plan tanj^ents; and the lines A J and 
J F represent the tangents on the cutting plane. Make D K equal BJ; draw K L parallel to A D; 
connect J L: then J L will be a level line on the cutting plane. Make L 1 parallel to E D; 
connect I B: then I B will be the direction of level lines on the horizontal plane common to both 
planes. At any point on the curve P draw P 0 parallel to I B; draw 0 H parallel to B J; make 

H M parallel to J L and equal to 0 P, and J N equal B Q; through A N M F trace a curve on 

the cutting plane which will lie perpendicularly over the plan curve A Q P C. 

Fig. 2. Construction of a Paper Representation of a Solid with its Angles, Surfaces, 
and Curved Lines as Given in Perspective and Described at Fig. i. —Let A B C D be the 
given form of base, and A H G C an eccentric or elliptic curve to which the sides A B and B C of 
the solid are tangent. At riglit angles to A B draw B U, C N and DM; at right angles to B C 
draw B E, C S and D L; let B U A be the angle of inclination required over the base or plan 
tangent A B; make B E and C R equal B U; let R S E be the angle of inclination required over 
the base or plan tangent B C; make D L, D M and C Q each equal R S; connect L A; make Q N 
equal B U; connect N M; make D K equal B U, draw J I parallel to D L, connect I B. At right 
angles to B I througli C and A draw A P'and CO indefinitely. On B as centre with E S as 
radius describe an arc at 0 ; again on B as centre with U A as radius describe an arc at P; 
then P 0 will be the distance over A and C on the cutting plane. On.U as centre with E S as 
radius describe an arc at X. On A as centre with P 0 as radius intersect the arc at X; on A 
with A J as radius describe an arc at V; and again on A with A L as radius describe an arc at W. 
On U as centre with B I as radius intersect the arc at V; connect A V W, W X, XU and U V; 

make UY equal ET; parallel to U V draw Y 2 ; make Y 2 equal F G, and UZ equal BH; through 

A Z 2 X trace a curve on the cutting plane,that will lie perpendicularly over the plan curve A H G C 
on the base. With a sharp-pointed instrument scratch the lines A B C D and A U; cut out the 
remainder of the figure and touch the adjoining edges with a little glue or thick mucilage and 
bring them together, leaving all lines on the outside so that their connections may be seen and 
understood. 

Fig. 3. Plan of Hand-rail, an Eccentric or Elliptic Curve, the Tangents of Unequal 
Length and Two Different Angles of Inclination. —Let C P B and B Q A be the angles of 
inclination over the plan tangents C B and B A. Make A L parallel and equal to B C; make 
P M equal B Q; parallel to C B draw M F; parallel to C P draw F G; connect G L: then G L 

will be the direction of a level line common to both planes. Parallel to G L draw J K, E B W 

and U S; parallel to C P draw I N; parallel to B Q draw T 6. At right angles to G L through 
C and A draw C D and A H indefinitely. On B as centre describe tlie arc P D; again on B as 
centre with Q A as radius describe an arc at H; connect H D: then H D will be the distance on 

the cutting plane over A and C, and if lines are drawn from D and H to B, D B and H B will 

then be tlie length and angle of tangents on the cutting plane. 

To Find the Angle for Squaring the Wreath-piece at the Joint over C:—Prolong the 
tangent B C to Z; prolong the joint-line C J until it meets the continuation of the level line G L 
at Y; make C Z equal M 0 ; connect Z Y: then the bevel at Z will give a plumb-line on the butt- 
joint over C. 

To Find the Angle for Squaring the Wreath-piece at the Joint over A:—Prolong the 
joint-line AU until it meets the continuation of the level line B 2 at W; prolong the tangent B A 
to X; make A X equal B R: then the bevel at X will give a plumb-line on the butt-joint over A. 

Fig. 4. Face-mould over the Plan of Hand-rail Given and Described at Fig. 3. —Make 
A B equal H D of Fig. 3. Make B E equal D 5 of Fig. 3. On E as centre with 5 B of Fig. 3 as 
radius describe an arc at C; on B with B P of Fig. 3 intersect the arc at C, and if the work is 
correct A C will equal A Q of Fig. 3. Connect CEP, B C and A C; make B F K equal P N F of 
Fig. 3; make A M equal A 6 of Fig. 3; parallel to E C draw G F J. Q K and N M L; make FJ, 
F G equal IK, I J of Fig. 3; make K Q equal G 3 of Fig. 3; make C D, C P equal E B, B 2 ; make 
M N, M L equal T S, T U of Fig. 3; through A draw L 0 ; make AO equal A L; through B draw 

G H; make B H equal B G; through H J D N 0 of the convex and G Q P L of the concave trace 

the curved edges of the face-mould. The joints A and B are at right angles to the tangents. 
The slide-line may be drawn anywhere on the face-mould, but must always be made at "right 
angles to the level lines. It is a matter of convenience to draw the slide-line from the centre of 
either joint of the face-mould. 

Fig. 5. To Find a Common Angle of Inclination Over Two Different Lengths of 
Plan Tangents when Required, the Total Height being Given;— The tangents are of the 
same lengt.h and angle as those of Fig. 3. Let C D equal boili C P and C Q of Fig. 3. Prolong 

C B indefinitely; on B as centre with B A as radius describe the arc A F; connect D F; parallel 

to F D draw B E; parallel to C D draw B H; at riirht angles to A B draw B G; make B G equal 
B H; connect G A; then tlie angle of inclination B G A is the same as the angle CEB. In this 
case the angle for squaring the wreath-piece will be alike for both joints. 


Plate: No. 17. 



Fig. 4 . 






























































































































PLATE 18. 

Fig. I. Represents a Solid Block or Prism Standing Vertically on a Base of the 
Given Form A B C D, the Sides of which are Equal and Parallel and have Two Acute 
and Two Obtuse Angles.—The acute angle formed by the position of the sides A B, B C of the 
base is intended in this case to represent the angle of plan tangents, embracing in the plan 
a curve of more than a quarter-circle. The upper end of the solid is shown as cut on the side 
A B, on the angle of inclination B F A, and on the side B C, on the same angle of inclination 
M G F. The sides of this solid being cut on a common angle of inclination, the heights from 
the base D E and B F are alike, and therefore a line drawn on the cutting plane from F to 
E will be a level line; and at the base—or horizontal plane—a line drawn from D to B will 
be the position of a level line common to both planes. Over the base A B and B C the lines 
A F and F G represent the tangents on the cutting plane,—or those of a face-mould. At any 
points on the curve at the base parallel to B D draw Q R and L K; through R and K par¬ 
allel to B F draw R I ; parallel to F E draw I H and T N ; make T N equal R Q. F J equal 

B 0 , and I H equal K L ; through A N J FI G trace a curve on the cutting plane which will lie 

perpendicularly over the plan curve A Q 0 L C. 

Fig. 2. Construction of a Paper Representation of a Solid with its Angles, Surfaces, 
and Curved Lines as Given in Perspective and Described at Fig. i.—Let A B C D be the 
form of base the opposite sides of which are parallel and equal. Draw A M and C M at right 
angles to B C and B A ; on M as centre describe the plan curve A C, which is greater than a 

quarter-circle. At right angles to A B draw B U, C F and D I ; at right angles to B C draw C G, 

B FI and D X ; let D X A and B U A be the common angles of inclination ; make B FI, C J, J G, 

C 4 , 4 F and D 1 each equal B U ; connect G FI and FI. As D I and B FI are of equal heights, a 

line from D to B will be the position of a level line common to both planes. Through C A 
draw tlie line P E indefinitely ; on B as centre with U A as radius describe an arc at P and 
at E ; then P E will be the distance over A and C on the cutting plane. At any points on the 
curve, as Q and R, parallel to M B draw Q 0 and L R; parallel to C G draw L K ; parallel 
to B U draw 0 S. On U as centre with P E as radiuS describe an arc at V; on A as centre 

with A X as radius intersect the arc at V ; again, on V as centre with the same radius describe 

an arc at W ; on U with FI G as radius intersect the arc at W ; connect A V, V W, W U and 

U V ; make U 2 equal FI K ; parallel to U V draw S T and 2 Z ; make S T equal Q 0 , U Y 

equal B N, and 2 Z equal L R; through the points W Z Y T A trace a curve that will lie per¬ 
pendicularly over the plan curve A Q N R C. With a sharp-pointed instrument scratch the 
lines A B C D A and A U ; cut out the remainder of the figure and touch the adjoining edges 
with a little glue or thick mucilage and bring them together, leaving all lines on the outside, 
so that their connections may be seen and understood. 

Fig. 3. Plan of Hand-rail Greater than a Quarter-circle; the Tangents to have a 
Common Angle of Inclination C F B over the Tangent C B, and B K A over the Tangent 
B A. Through A and C draw the line D E indefinitely ; on B as centre with B F as radius 
describe the arc F E ; and again on B with the same radius as before describe an arc at D : 
then D E will be the distance over A C on the cutting plane; and if lines are drawn from D 
to B and from E to B, then D B and E B will be the length and angle of tangents on the 
cutting plane. J B will be the direction of a level line common to both planes. Parallel to 

J B draw L 0 and C P ; parallel to C F draw N G. 

To Find the Angle for Squaring the Wreath-piece at Both JointsProlong the tan¬ 
gent B C to FI ; make C H equal C G ; connect H J : then the bevel at H will give a plumb- 
line on the butt joints over A and C. 

Fig. 4. Face-mould over a Plan of Hand-rail Greater than a Quarter-circle, the Tan¬ 
gents having a Common Angle of Inclination as given at the Plan Fig. 3.—Let V X U 
equal D T E of Fig. 3. On V as centre with B F of Fig. 3 as radius describe an arc at W ; 
and on U as centre with the same radius as before intersect the arc at W ; connect V W, U W 
and X W : X W should equal T B of Fig. 3. Make V C and U G each equal F G of Fig. 3 ; par¬ 
allel to W X draw V E, C B A, G H F and U K ; make V E and U K each equal C P of Fig. 3. 
Make C B and C A equal N 0 and N L of Fig. 3 ; and again, make G FI and G F equal N 0 
and N L of Fig. 3. Through U draw F J indefinitely; through V draw A D indefinitely; make 
V D equal A V; make U J equal U F; make W Z Y equal B Q S of Fig. 3. Tiie points V and 
U are at right angles to the tangents. Through DEBZFIKJ of the convex and A Y F of the 
concave trace the curved edges of the face-mould. 

Fig. 5. Parallel Pattern for Round Rail, or to be Used Instead of the Face-mould 
as a Means of Saving the Width of Stuff for Marking the Wreath-piece on the Rough 
Plank.—Make DTE equal D T E of Fig. 3; make EB and DB each equal F B of Fig. 3; 
connect B T, B D and B E ; make E N and D N each equal F G of Fig. 3; make N M, N M 
each equal N M of Fig. 3 ; make B R equal B R of Fig. 3. Describe circles on the points 
E M R M D as centres of any required radius for width of pattern. Bend a flexible strip of 
wood or other material by which to mark curve-lines touching the circles for the convex and 
concave edges of the pattern. The joints are made at right angles to the tangents. 



I 








































































































































1 


PLATE 19. 

Fig. I. ’Represents a Solid Block or Prism Standing Vertically on a Base of the 
Given Form A B C D, the Sides of which are Equal and Parallel and have Two Acute 
and Two Obtuse Angles. —The acute angle formed by the position of the sides A B, B C of 
the base is intended in this case to represent the angle of plan tangents embracing in the plan 
a curve of more than a quarter-circle. The upper end of the solid is shown as cut on the side 
A B on the angle of inclination B F A, and on the side B C on a less angle of inclination M G F. 

To Find the Position of a Level Line on the Cutting Plane; —Make BN equal D E; 
draw N H parallel to A B; connect H E, which is the level line sought; parallel to B F draw HJ: | 

then the line D J on the horizontal plane will be the position of a level line common to both planes. At j 

any points on the curve at the base parallel to J D draw 0 R and L K; through R and K 
parallel to B F draw R S and K U; parallel to H E draw U T and S P; make U T equal K L, 

S P equal R 0 , and H Q equal J X; through the points A P Q T G trace a curve on the cutting 

plane which will lie perpendicularly over the plan curve A 0 X L C. 

Fig. 2. Construction of a Paper Representation of a Solid with its Angles, Surfaces, 
and Curved Lines as Given in Perspective and Described at Fig. i. —Let A B C D be the 
form of base the opposite sides of which are parallel and equal. C X and A X are at right 
angles to A B and B C. On X as centre describe the plan curve A W C, which is greater than a 
quarter-circle. At right angles to A B draw B E, C L and DM; at right angles to B C draw B F, 

C H and D N; let B E A be the angle of inclination over BA; make B F and CJ each equal B E; 
let J H F be an angle of inclination—over C B—less than B E A over B A; make D N, D M and 
C K each equal J H; make K L equal B E; connect L M and N A; make B 5 equal D N; draw 

5 U parallel to B A, and U V parallel to E B: then a line drawn from V to D will be the position 

of a level line common to both planes. At right angles to D V draw A Q and C P; on B as 
centre with F H as radius describe an arc at P, and again on B as centre with E A as radius 
describe an arc at Q: then Q P will be the distance over A C on the cutting plane. At any 
points on the plan curve Y and J draw J 1 and Y 0 parallel to D V; make I G parallel to C H; 
make V U and 0 Z parallel to E B; on U as centre with V D as radius describe an arc at R; on 
A with A N as radius intersect the arc at R; on E as centre with F H as radius describe an arc 

at S; on A as centre with P Q as radius intersect the arc at S; connect A R, R S, S E and UR; 

make E T equal F G; parallel to U R draw Z 2 and T 4 ; make Z 2 equal 0 Y, U 3 equal V W, and 
T 4 equal I J; through the points S, 4 , 3 , 2 A trace a curve on the cutting plane that will lie 
perpendicularly over the plan curve A Y W J C. With a sharp-pointed instrument scratch the lines 
A B C D A and A E; cut out the remainder of the figure and touch the adjoining edges with a i 

little glue or thick mucilage and bring them together, leaving all lines on the outside, so that ] 

their connections may be seen and understood. f 

Fig. 3. Plan of Hand-rail Greater than a Quarter-circle, the Tangents to have Two ? 

Different Angles of Inclination: BZA over the Plan Tangent A B, and a Less Angle ) 

of Inclination C H B over the Plan Tangent C B.—Make A 4 parallel and equal to B C; 
make B 5 equal C H; draw 5 L parallel to A B, and L V parallel to Z B: then the line V 4 will be f 

the direction of a level line common to both planes. Parallel to V 4 draw S U, B F and Q X; ' 

draw Y N parallel to Z B, and TJ parallel to C H. j 

To Find the Angle for Squaring the Wreath-piece over the Joint C:—Prolong ^ 

the tangent B C to G; make C G equal C D; connect G F: then the bevel at G will give a plumb- ' 

line on the butt-joint over C. 

To Find the Angle for Squaring the Wreath-piece over the Joint A:—Make E R 
parallel to B A and equal to V M; connect R A: then the bevel at R will give a plumb-line on 
the butt-joint over A. Through C and A at right angles to V 4 draw C 1 and A K indefinitely; 

on B with B H as radius describe the arc H I; and again on B as centre with Z A as radius •: 

describe an arc at K; connect K I; then K I will be the distance over A and C on the cutting 

plane; and if lines are drawn from K to B, and I to B, then I B and K B will be the length and 

angle of tangents on the cutting plane or, which is the same thing, of the face-mould. 

Fig. 4. Face-mould over a Plan of Hand-rail Greater than a Quarter-circle, the 
Tangents having Two Different Angles of Inclination as Given at the Plan Fig. 3.— 

Make H C A equal I 0 K of Fig. 3. On C as centre with 0 B of Fig. 3 as radius describe an arc 

at B; on H as centie with H B of Fig. 3 as radius intersect the arc at B: then if the work is 

correct A B will equal A Z of Fig. -3. Connect A B, B H and C B; make H N equal H J of 

Fig. 3; make B Q K equal Z L N of Fig. 3; parallel to C B draw N F, N 0 , Q L and K J, K D; 

make N 0 , N F equal T U, T S of Fig. 3; make Q R L equal V W P of Fig. 3; make K J, K D 

equal Y X, Y Q of Fig. 3; through A draw D E; make A E equal A D; through H draw F G; 

make H G equal H F. The joints H and A are at right angles to the tangents. Through G 0 R J E 

of tlie convex and F L D of the concave trace the curved edges of the face-mould. J'he slide¬ 
line in this case ajid of all face-inoulds of whatever character is always at right angles to the level line. 



No. ] 9. 


Pl. 



H 



Fig. 3. 































































































































































PLATE 2 0. 

Skilful workers of hand-rail know that carefully shaping the wood next the joints of a 
wreath-piece so that it will nicely fall in with its adjoining pieces, of whatever character they 
may be, is of the first importance ; next, experience has taught them that the interval the 
helical surfaces—or top and bottom surfaces between joints, compel them to follow certain 
curvatures peculiar to each kind of wreath-piece. From these facts of experience it is evident 
that a face-mould is not only a means of shaping the sides of a wreath on the plane of the 
plank, but that it carries with it certain geometrical curves that shape the top and bottom 
surfaces of the wreath. This controlling curve-line of helical surfaces of wreaths is a centre 
line,* as at A E R, Fig. 2, and is found in the development of the central cylindric line on cut¬ 
ting planes as Z J U of Fig. i, Plate No. ii, and C 0 Q S E of Fig. i, Plate No. 10. See also 
the similar cases of the two last solids referred to, with their cutting planes brought in posi¬ 
tion over the plan at their bases. Fig. 6, Plate No. ii. A round hand-rail—controlled from 
its centre as it properly must be—over a circular or curved plan affords a complete demon¬ 
stration that this centre cylindric line gives shape to the top and bottom of the rail, for 
while its curved sides hang vertically over the plan, its top and bottom also take proper 
curves, forming its own easings perfectly suited to the requirements of every case. To meas¬ 
ure and make an exact drawing of this centre line will demonstrate' the peculiar form of 
curvature in all cases of wreaths, and also show exact heights at every point over an eleva¬ 
tion of treads and rises embraced within any curved plan. Thus the practical use of develop¬ 
ing the centre line will be to get the length of balusters in any position as required on wind¬ 
ing steps in cylinders; also the ability to test the wreath-piece over the elevation, and 
determine when desirable what changes to m;ike, if any, in the inclination of tangents. 

Fig. I. The Semicircle ACM is a Plan of the Centre Line of a Hand-rail with 

Tangents to Each Quarter A B, B C and C N, N M.—In this plan the two quarters that 

make the semicircle are of the same character as the first two solids introduced. The first 
solid at Plate No. 10 is here repeated by D M N C ; the other, D A B C, at Plate No. ii. 
At Plate No. ii, Fig. 6, two similar solids are brought together showing the difference in 
their cutting planes as placed in position over the plan of a semicircle at the base. The 
quarter-circle A C over its tangents A B, B C has a common inclination B Y A, C E B ; also the 
quarter-circle M C over one tangent C N has the same inclination N R C, while the tangent 
M N remains level. On the quarter A C, B D is the position of a level line common to both 
planes, as before shown ; and on the quarter C M, N M is the level line common to both 
planes. Divide the quarter-circle A C, and the quarter C M, each into four equal parts ; through 
L and H draw LJ, H G parallel to the level line D B; parallel to C E draw G F; parallel to 
B Y draw J K ; through 0 , P, Q parallel to the level line M N di aw 0 S, P T and Q U. 

Fig. 2. Development or Unfolding of the Centre Line of a Semicircular Wreath of 
Hand-rail over the Plan A C M as given at Fig. i.—Draw A X ; make A L 1 equal A L I of 
Fig. i. Draw 1 Y at right angles to A X ; make I Y and L K equal J K and B Y of Fig. 1. 
Parallel to A X draw Y C; make Y H C equal I H C of Fig. i ; draw C E and H F at right 
angles to A X ; make H F and C E equal G F and C E of Fig. i. Parallel to A X draw E N ; 

make E Q P 0 N equal C Q P 0 M of Fig. i. Through N at right angles to A X draw X R ; 

make N R, 0 S, P T and Q U at right angles to E N and equal to N R, V S, W T and X U of 
Fig. I. Through the points AKYFEUTSR trace the centre line sought.f 

Fig. 3. The Semicircle Q V S is the Plan of a Centre Line of Hand-rail with Tan¬ 
gents to each Quarter Q U, U V and V W, W S.—Let U T Q be the inclination required over 
the plan tangent Q U, and V Y U the greater inclination required over the plan tangent U V ; 
and for the quarter S V the angle WAV must be the same as V Y U ; the plan tangent W S 

remains level. To find the level line for the quarter Q V, let Y X equal U T; draw X Z par¬ 

allel to V U, and Z F parallel to Y V ; connect F R, which is the level line sought. Divide V J 
in two parts ; parallel to F R draw U K; divide K Q into three parts ; divide V S into four 
parts ; parallel to the level line S W draw P B, 0 C and N D ; parallel to R F draw H G, L 8 

and M 6; parallel to V Y draw G E ; parallel to U T draw 8, 4 and 6 , 5 . See Plate No. 12 

/or case of solid like R Q U V of Fig. 3. 

Fig. 4. Development of the Centre Line of a Semicircular Wreath of Hand-rail 
over the Plan Q V S as given at Fig. 3.—On the line Q F make Q M L K equal Q M L K 
of Fig. 3. Erect the perpendiculars K T, L 4 and M 5 equal to U T, 8, 4 and 6, 5 of Fig. 3. 
Draw T V parallel to Q F ; make T J H V equal K J H V of Fig. 3 ; perpendicular to Q F draw 

V Y, H E and J Z ; make V Y, H E and J Z equal V Y, G E and F Z of Fig. 3 ; parallel to Q F 

draw YW ; make Y N 0 P W equal V N 0 P S of Fig. 3 ; through W at right angles to Q F 
draw F A ; make W A, P B, 0 C and N D equal W A, 3 B, 2 C and I D of Fig. 3. Through the 
points Q 54 TZEYDCBA trace the centre line sought. 

Fig. 5. This Portion of a Circle Less than a Quarter is a Plan of a Centre Line of 
Hand-rail with its Tangents D C and C B.—Over the plan tangent DC let DEC be the 
angle of inclination required, the tangent C B to remain level. Divide the curved line B D 

into any number of equal parts, and from the points of division J I H G F draw lines par¬ 
allel to B C and touching D C ; at right angles to D C draw 0 P, N Q, M R, L S and K T. 

Fig 6. Development of the Centre Line of a Wreath-piece over a Plan of a Portion 

of a Circle less than a Quarter as given at Fig. 5.—On the line D B make D F G H I J B 
equal the spaces between the corresponding letters at Fig. 5. Make D E, F T, G S, H R, I Q 

and J P equal D E, K T, L S, M R, N Q and 0 P of Fig. 5. Through the points B P Q R S T E 

trace the centre line sought. I'he solid Fig. 5 is given in detail at Plate No. 13. 

* The tangents are invariably placed at the centre of the width, and the heights and angles of inclination are 

also always at the centre of the thickness of the wreath-piece. 

f A practical self-imposed useful lesson would be to make thd two solids composing Fig. i of wood, and glu¬ 
ing them together in the manner shown at Fig. 6. Plate No. ii, remove the wood to the semicircle at the 
base and its vertical trace on the cutting planes ; then wrap Fig. 2 , the development, around the cylindric surface 
of Fig. I, and test the curve thus obtained. 




P L AT E No. 2 0 . 









































PLATE 21. 

Fig. I. Plan of a Centre Line of Hand-rail Greater than a Quarter-circle; the 

Tangent B C to have an Angle of Inclination Equal to C D B, the Other Tangent B A to 
Remain Level. —Divide the circular line A C into any number of equal parts, and from each of 
these points of division draw lines parallel to the level line A B touching the tangent B C, as 
0 V, E F, G H, L K and M N; parallel to C D draw N P, K J, HI, F S and V W. This solid is given 
at Plate No. 14. 

Fig. 2. Development or Unfolding of the Centre Line of a Wreath-piece over a 
Plan Greater than a Quarter-circle as given at Fig. i.—On the line AC make AOEG LMC 
equal the spaces between the corresponding letters of Fig. i. At right angles to A C draw C D 
equal to C D of Fig. i. Make M P, L J, G I, E S and 0 W parallel to C D and equal to N P, K J, 
H I, F S and V W of Fig. i. Through A W S I J P D trace the centre line sought. 

Fig. 3. Plan of a Centre Line of Hand-rail Greater than a Quarter-circle, the 

Tangents Q T and T X to have the Common Angle of Inclination X Y T and T Z Q.— 
Divide the circular line Q X into any even number of equal parts, and from each of these points 
of division draw lines parallel to the level line R T touching the tangents, as I J, G H, D E and 
A B; make J K and H L parallel to X Y, and E M and B C parallel to T Z. This solid is given at 
Plate No. 18. 

Fig. 4. Development of the Centre Line of a Wreath-piece over a Plan Greater 
than a Quarter-circle as given at Fig. 3. —On the line Q P let Q A D F equal the spaces 
between tlie corresponding letters of Fig. 3. At right angles to Q F draw F Z, D M and AC 

equal to T Z, EM and B C of Fig. 3. Make Z X parallel to Q P; make Z G I X equal F G I X of 

Fig. 3; througli X draw Y P at right angles to Q P; make I K and G L parallel to XY; make 
X Y, I K and G L equal X Y, J K and H L of Fig. 3; through Q C M Z L K Y trace the curve sought. 

Fig. 5. Plan of a Centre Line of Hand-rail Greater than a Quarter-circle, the 
Tangents to have Different Angles of Inclination; the Angle DCF over the Plan 
Tangent D F, and a Less Angle of Inclination F E A over the Plan Tangent A F.—To find 
a level line common to both planes: draw A B parallel and equal to F D; make C L equal F E; 

draw L J parallel to D F; make J I parallel to DC: then the line I B tvill be the level line sought. 

From F draw F P parallel to I B; divide P A and 0 D each in two equal parts; draw Q H and 

N M parallel to IB; make M K parallel to D C, and H G parallel to F E. This solid is given at 

Plate No. 19. 

Fig. 6. Development of the Centre Line of a Wreath-piece over a Plan of More 
than a Quarter-circle, the Tangents having Different Angles of Inclination as given at 
Fig. 5.— On the line A R make A Q P equal A Q P of Fig. 5; make P E and Q G perpendicular 
to A R and equal to F E and H G of Fig. 5; draw E D parallel to A R; make EO N D equal 
POND of Fig. 5; through D draw C R at right angles to A R; draw N K and 0 J parallel to 

D C; make D C, N K and 0 J equal D C, M K and I J of Fig. 5; through the points AG E J KC 

trace the centre-line sought. 

Fig. 7. Plan of a Centre Line of Hand-rail Less than a Quarter-circle, the 
Tangents S U and U V to have the Common Angle of Inclination VXD and U W S.— 
Make S T parallel and equal to U V: then T U will be a level line common to both planes. 

Divide the curved line SV into any even number of equal parts SADKGYV; parallel to T U 

draw Y Z, G H, D E and A B; parallel to V X draw Z J and H I; make E F and B C parallel to 
U W. This solid is given at Plate No. 15. 

Fig. 8. Development of the Centre Line of a Wreath-piece over a Plan of Less 
than a Quarter-circle, the Tangents having a Common Angle of Inclination as given at 
Fig. 7. —On the line S L make S A D K equal S A D K of Fig. 7; at right angles to S L make 

K W, D F and A C equal U W E F and B C of Fig. 7; draw W V parallel to S L; make W G Y V 

equal K G YV of Fig. 7; through V at right angles to S L draw XL; parallel to L X draw Y J 

and G I; make V X, Y J and G I equal V X, Z J and H I of Fig. 7; through the points SC F W I J X 

trace the centre line sought. 

Fig. 9. Plan of a Centre Line of Hand-rail Less than a Quarter-circle, the Tangents 
to have Different Angles of Inclination; P R M over the Tangent, M P and N Q P a Less 
Angle of Inclination over the Tangent P N.—Make P S equal N Q, and ST parallel to P M; 
make TV parallel to R P; from M parallel and equal to P N draw M 0 : then OV will be a level 
line common to both planes. Divide B M in two equal parts M A B; draw P C parallel to V 0 ; 
divide C N into three equal parts C D E N; parallel to 0 V draw E F, D G and A U; parallel to N Q 

draw F I and G H; parallel to P R draw U J. This solid is given at Plate No. 16. 

Fig. 10. Development of the Centre Line of a Wreath-piece over a Plan of Less 
than a Quarter-circle, the Tangents having Different Angles of Inclination as given at 
Fig. 9. —On the line M F make M A B C equal M A B C of Fig. 9; at right angles to M F make 
C R, B T and A J equal P R, V T and U J of Fig. 9; draw R N parallel to M F; make R D E N 
equal C D E N of Fig. 9; through N draw F Q at right angles to M F; parallel to N Q draw El 

and D H; make N Q, E I and D H equal N Q, FI and G H of Fig. 9; through the points 

M J T R H I Q trace the centre line sought. 


P LATE No. 21. 









































PLATE 22. 

Position of Riser in Connection with Cylinders at the Landing and Starting of Straight 
Flights of Stairs.—The Face-mould, and the Management of the Wreath-pieces. 

Fig. I. A Sufficient Elevation of Rises and Tread to Determine the Place of Riser 
at the Bottom of a Flight when the Over-wood is to be all Removed from the Top of 
the Wreath-piece, as in this Case. —Let X X be the centre of the short balusters and the 
bottom line of the liand-rail; make X B the thickness of rail, and X C = the thickness of 
plank; draw C E parallel to X X ; make X A half the thickness of plank ; draw A D parallel 
to X X ; make N F four inches, and F D half the thickness of the rail, i^", being all together, from 
the floor to S, 5^". Where the centre line A D intersects the centre level line S D, that inter¬ 
section at D fixes the centre of wreath-piece as shown. From D parallel to the riser draw 
D G indefinitely; anywhere below the floor-line and parallel to it draw K G ; as G is the 
centre of the rail, G 0 must be a half-inch to the face of the cylinder ; and as the diameter 

of the cylinder is 6 ", 0 K must be 3"; draw K L parallel to the riser ; continue the line of 

the first riser to H ; on K with K 0 for radius describe the cylinder : then H J shows the 

distance to be between the bottom riser and the commencement of the cylinder; and this 

is so placed at the plan Fig. 3, as may be seen by the corresponding letters. 

Fig. 2. Elevation of Tread and Rise at the Top of a Flight Sufficient to Determine, 
when all the Over-wood is Removed from the Bottom of a Wreath-piece, the Relative 
Position of the Riser and Cylinder. — At the bottom —Fig. i— all the over-wood, B C, is taken 
off the top of the straight part of the wreath-piece ; not, however, because it is the top, but 
because it is the concave face; and in cases of this kind it makes the best shape either for 
the top or the bottom of the flight. At the top of the flight this over-wood is taken off at 

the bottom side of the wreath-piece. This is so because the bottom wreath-piece is simply 

turned the other side up at the top of the flight, but the over-wood is still taken from the 
concave face. The position of the cylinders differ; at the bottom of the flight the chord¬ 
line of the cylinder is from the face of the riser, and at the top of the flight it is 2". 

The letters at the various points of this elevation are made to correspond with those of Fie. i, 

so that having examined and made the drawings of that figure, a careful inspection of this 
will be all the explanation needed. 

Fig. 3. Plan of the Bottom of Flight with the Riser and Cylinder as Determined 
at Fig. I. 

Fig. 4. Plan of the Top Portion of Flight with the Cylinder and Riser Placed as 
Determined by the Trial at Fig. 2.—Of the plan of hand-rail around the cylinder, one 
quarter-circle has to be prepared for drawing a face-mould. Q X and X G are the plan tan¬ 
gents to the centre line of rail, the pitch-board to be placed as shown; continue G X to W ; 
parallel to G X draw A V, Z T and K Y R. 

Fig. 5. Face-mould.—* Draw FW indefinitely; make WVTR equal WVTR of Fig. 4, 
At right angles to F W draw W B, V A, T 0 Z and R E Y ; make W B equal X G of Fig. 4. 

Through B draw A D parallel to R W ; make B D equal B A ; make B C equal G C of Fig. 4 ; 

make T O, T Z, R E, R Y each equal S 0 , S Z and Q Y, Q Y of Fig. 4; parallel to R F draw Y M 

and E L; through D C 0 E of the convex and A Z Y of the concave trace the curved edges 

of the face-mould. In this connection is shown the laying out of joints B and F to square 
the wreath-piece. 

Fig. 6. Perspective Sketch of the Wreath-piece, showing both joints prepared for 
squaring, and the application of the face-mould to both sides of the stuff. 

Fig. 7. Elevation of Tread and Rises for the Top and Bottom as before Given, 
the Object being to show that sometimes by a Change in Removing the Over-wood 
the Wreath-piece may be Kept in its Required Position as to Height and the Chord¬ 
line of the Cylinder Brought to the Face of the Riser.—G is the centre of the rail, G 0 
is ; O K is the radius of the cylinder. The height from the floor to D is fixed as before, 
alike at the bottom and at the top. The bottom line of rail must pass through X X, the 
centres of the short balusters ; from X X set off the thickness of rail 2^"; and from D, which 
must be at the centre of the plank, set off both ways half the thickness of plank parallel to 
X X : this will show how the over-wood must be removed from the straight part of each wreath- 
piece.f The bottom of the rail at the ce 7 ttre of the wreath is kept 4" above the floor to suit the 
required length of balusters on the level. At X X the short balusters are 2'.2" from the top of 
the step to the bottom of the rail ; then from the floor to the bottom of the level rail the 
height will be 4" more, equal to 2'.6", the same length that the longest baluster on each step 

has to be, because being half a tread back from the short baluster, it must therefore be a 

half-rise longer. The merchantable lengths of ordinary balusters are 2'.4" and 2'.8", thus allow¬ 
ing one inch to go in the rail and one inch to dovetail in the step. The illustrations giveti 
at Figs, i, 2 a 7 id 7 as methods of working wreath-pieces and disposing of the over-wood on the 
straight part are not to be understood as applying only to 6 " cylinders; for after fixing the required 
position of wreath-piece, and G and 0 , then 0 K may be any radius of cylinder, more or less. 
For instance, in the case of Fig. i, if 0 K, instead of being a radius of 3", should be 6", then 

the riser would set into the 12" cylinder. And again, if instead of 0 K being 3", it should 

be 2" radius, then there would be 2^" straight between the riser and the chord-line of a 
4" cylinder. 

Note.—I t must be understood that throughout this work, with the exception of the cases given at Plates 34 and 

35, all joints of wreath-pieces are to be made at right angles to their tangents, and square through the face of the 

plank. 

* At Plate No. 10 are given perspective and geometrical drawings, and the formation of a paper representation of 
a solid, a plan of hand-rail, and from it a drawing of a face-mould, which together give a complete practical knowl¬ 
edge of the application and drawing of face-moulds of this kind. 

t At Fig. 7 about all that can be done further—if desirable—within the limits of the thickness of the plank will be 

at the top of the flight to take all the over-wood off the top of the wreath-piece, and at the bottom of the flight lake 

all the over-wood oft the bottom of the wreath-piece; this change would bring D at the bottom of the flight—keeping 
it at the same Lfiorht, about nearer to the riser; and D at the too, about i" nearer to the riser, at the same height. 



Plate No. 22 . 
















































































































PLATE 2 3. 

Platform Stairs, Half-turn, or Such as given by Plan and Elevation at Plate No. i. Figs. 
3 AND 4. — The Position of Cylinder with the Place of Connecting Risers, and the 
Differences Possible by Varying the Removal of Over wood from the Straight Portion 
OF Wreath-pieces; also How to Fix the Risers Connecting with the Cylinder, so 
that the Whole Wreath may have One Common Inclination, besides Saving Several 
Inches of Stepping-room. 

Fig. I. Elevation of Rises and Treads Above and Below the Platform to Test the 
Removal of Over-wood from the Wreath-pieces.—The bottom line of rail must in all cases 
pass through the centres of the short balusters X X. As the rail is to be 2\" thick by 4" wide 
the plank out of which the wreath-pieces are to be worked must be 4" thick. Make X B and 
B C each 2"; draw B D and C E parallel to X X; make X N and X M 2^"; connect N M; make 
R U half a rise. 3!"; make U D half the thickness of rail, ij"; make D F and D S each 2", 

half the thickness of plank; make X J 2T', the thickness of rail; draw F L, J P and S Q parallel 

to X X. This drawing shows that keeping the rail above the platform at the height R U and 
taking all the over-wood off at N C of the upper wreath-piece, the lower wreath-piece must 
have of over-wood taken off at J L, the top, and 1" off the bottom, X Q. From D parallel 
to the line of riser draw D G; at right angles to D G draw G K; make G 0 , h", and 0 K, 3", the 
radius of the cylinder; on the centre K describe the cylinder Y A; parallel to D G through 
K draw Y V, and continue the line of risers to T Z: then A T will be the distance between the 
chord-line of the cylinder and the face of the risers at the platform. Another change can be 
made by taking all the over-wood off the bottom of the lower wreath-piece, and this would bring the 
riser of that side f" further from the chord-line of the cylinder—all together 2^". 

Fig. 2. Elevation the Same as that of Fig. I.— The object in repeating this drawing 
is to call attention to still another change in removing over-wood. In this case the over-wood 

is ail taken off the bottom of the upper wreath-piece, and off the top of the lower wreath- 

piece, bringing the chord-line of the 6" cylinder to the face of the riser as shown. An inch 
variation in the height of R U to bring the over-wood as required would be of slight importance. 
This arrangement of wreath-pieces and over-wood is not corifitied to any size of cylinder; for instance, 
if the cylinder is to be 12" diameter, then, G 0 being fixed points, 0 K would be 6", and the 
risers would set just as they are, but would be in the cylinder 3". At Fig. i a similar change 
would take place if the size of cylinder is altered; that is to say, that, G 0 being fixed, if 
the radius of the cylinder is made less, the chord-line would be drawn nearer 0; and if the 
radius is made greater, the chord-line of the cylinder advances further towards the risers and 
into the step, as the increase is more or less. The face-mould for Figs, i and 2 is to be found 
exactly as directed at Figs. 4 and 5 of Plate No. 22. 

Fig. 3. Here again is an Elevation of the Same Tread and Rise Connected with a 
Platform and the Same Size Cylinder as given at Figs, i and 2. —This elevation is 
introduced for the purpose of showing how, by a wholly different treatment, the wreath in 
this case, or indeed of any-sized cylinder—within reasonable limits—connected with a platform- 
stairs as given by plan and elevation at Plate i. Figs. 3 and 4, may be carried around such 
cylinder on one common inclination, saving room in the stepping, and making a superior shaped 
wreath. After setting up the elevation, begin by drawing the bottom lines of rail through 
the centres of short b.ilusters at X X; set off the centre line and the thickness of rail parallel 
to XX as shown. Draw H F indefinitely; make H N and N F each equal K G, 3T', the radius 
of a 6" cylinder, and more to the centre of rail and baluster; through F parallel to the 
riser-lines draw B S; through N draw MU; at M and J parallel to H F draw J E and M L: 
then the four heights C E, E F, F L and L B will be equal; anywhere on the line B S at K 

as centre with 3" = K 0 as radius describe the cylinder, and with V more radius to G describe 

the centre line of rail R G P; draw G W, P Q and R V at right angles to PR; make the 

heights Q T, GW, U V and R S each equal J N; connect S U, V G, W Q and T P: then the 

four heights and inclinations are set in proper relation to their base, the plan tangents. 

Fig. 4. Plan of Rail the Centre Line of which is the Quarter-circle K PG of Fig 3.—The 
heights and inclinations Q T P and G W Q are the same as those of like lettering at Fig. 3. 

Through Q draw S Z; parallel to Q Z draw F E and P B; through G draw P K; on Q as centre 

draw WK; parallel to Q T draw D C. 

To Find the Angle with which to Square the Wreath-piece at Both Joints:—Make 
G Y equal G X; connect Y Z: then the angle as taken by the bevel at Y will give a plumb- 
line—H G of Fig. 5—on the butt-joints, by means of which the wreath-piece may be squared. 

Fig. 5. Face-mould taken from the Plan Fig. 4; also Showing the Squaring of 
the Wreath-piece at Both Joints.—On the line K K make A K, A K each equal A K of Fig. 4; 
make A T at right angles to A K and equal to A Q of Fig. 4; connect K T, KT; make T C, T C 
each equal T C of Fig. 4; parallel to A T draw KB, KB, C E, C F, C E, C F; make K B, K B 

each equal P B of Fig. 4; make C E, C F, C E, C F equal D E and D F of Fig. 4; make T S 

and T R equal Q S and Q R of Fig. 4; through K, K draw the lines F D, F D; make K D, 
K D each equal F K; continue T K to L, and make K L any length desirable, or equal to A B 
or C D of Fig. 3; parallel to K L draw D 0 and F 0 ; make the joints L and K at right 
angles to the tangents. Through DBESEBD of the convex and F R F of the concave trace 
the edges of the face-mould. 

Note. —At Plate No. ii are given perspective and geometrical drawings and instruction how to form a paper 
representation erf a solid, also a quarter-circle plan of hand-rail, and irom this plan a drawing of a face-mould; and at 
Fig. 7 of that Plate an explanation of the line K G A P of Fig. 4 of this Plate—which together give a practical knowledge 
of the application and drawing of face-moulds of this kind. directions in detail for sliding face-moulds and the correct 
application of bevels for squaring ■wreath-pieces ■will bc found a,t PLATE No. 56. 





Plate No. 23. 




























































PLATE 24. 

Figs. I and 2. Starting and Landing Elevations Sufficient to Show the Position in 
the Cylinders of the Starting and Landing Risers. —The cylinders of 15" diameter; the over¬ 
wood to be removed from the straight part of wreath-piece the same as at Figs, i and 2 of 
Plate No. 22. 

Fig. 3. Face-mould from Plan of Hand-rail Fig. 2. —The lettering of face-mould and 
plan are alike; and as face-mould, plan, and elevations all have been before carefully explained 
at Plate No. 22 (the whole being drawn to a scale of iV to the foot), it will not be necessary 
to repeat the same here. 

Where the diameter-line of a large cylinder is placed at the face of a landing-riser it will 
be necessary to manage the case as explained through Figs. 4, 5 and 6.* Just here attention 
may as weli be called to the important fact that whenever it is desirable the whole radius of cylinders 
—such as are introduced in this Plate, and also of Figs, i, 2 and 7 of Plate No. 22, and Figs, i and 2 
of Plate No. 23 — may be saved or used for step-room, in an entirely u 7 iobjectionable and work 77 ia 7 tlike 
manner, if pla 7 t and wreath-piece are treated as directed at Plate No. 33. 

Fig. 4. Elevation of Tread and Rise Sufficient to Take Measurements with which 
to Prepare the Plan of Hand-rail for the Purpose of Drawing a Face-mould. —Draw the 
bottom line of rail through XX, the centres of short balusters; parallel to X X draw E D, the centre 
of the thickness of rail; make R U = 4", U D = from T draw T S parallel to the floor-line ; 
from D at right angles to the floor-line draw D S. 

5 - Plan of Hand-rail with the Top Riser Placed at the Diameter-line of a 15" 
Cylinder. —At the centre of the width of rail T, and at right angles to T K, draw the tangents 
TS indefinitely; from D of Fig. 4 parallel to the line of riser draw a line to S of Fig. 5; make 
SD equal SD of Fig. 4; connect DT; from S draw the line SMY tangent to the centre line 
of the plan of rail; from K at right angles to S Y draw the line K M; then M will be the joint 
of the wreath-piece, and the remainder of the rail around the cylinder from M to I will be level. 
Parallel to M S draw N J, 0 Q and T W; continue M S to A. From T at right angles to S M draw 

the line T Z indefinitely; on S with D T as radius describe an arc at Z. 

To Find the Angle with which to Square the Wreath-piece at the Joint over M:— 
Make M Y equal S D; connect Y W: then the bevel at Y will give the angle required. 

To Find the Angle with which to Square the Wreath-piece over the Joint T:—Prolong 
the tangent ST to L; make T L equal G V, and connect L J: then the bevel at L will give the 
angle required.f 

Fig. 6. Face-mould taken from the Plan Fig. 5, also Showing the Squaring of the 
Wreath-piece at Both Joints.J —On a line E D make DT equal D T of Fig. 5. T E may be 
any length for straight wood. On T as centre with Z M of Fig. 5 as radius describe an arc at 
M; on D as centre with S M of Fig. 5 as radius intersect the arc at M; connect M D and prolong 
M D to S; make TCP equal T C F of Fig. 5; parallel to M D tlirough F, C and T draw U N, 

R G and TB; make DS equal S A of Fig. 5; make FU and F N equal G H and G N of Fig. 5; 

make CR and C G equal BO and B Q of Fig. 5; make TB equal T P of Fig. 5; through T draw 
R 0 ; make T 0 equal T R; parallel to T E draw R H and 0 A; make the joints E and M at right 
angles to the tangents; make M K equal M N; through K S U R of the convex and N G BO of the 
concave trace the edges of the face-mould. The bevel at Y, showing the squaring of the wreath- 
piece at joint M, is taken from Y of Fig. 5; and the bevel at L, showing the squaring of the 
wreath-piece at joint E, is taken from L of Fig. 5. 

* Tlia method of proceeding would be the same at the bottom, or starting, of a staircase. 

f The angle required to square a wreath-piece at each joint is, in every case, the inclination of the plane of the plank 
along the joint given on that plane—which is the joint of the face-mould—and a plumb-line on the butt-joint—which is a 
joint made square from the face of the plank through its thickness. 

X At Pr.ATE No. 13 are given perspective and geometrical drawings, and instructions how to form a paper representation 
of a solid; also a plan of hand-rail less than a quarter-circle, and from this plan a face-mould—which, together, give a 
practical knowledge of the application and drawing of face-moulds of this kind. 



Plate No. 24. 















































































PLATE 25. 

Fig. I. Plan of the Top Portion of a Staircase Winding One Quarter, with a Small 
Cylinder as given at Plate No. 5, Fig. 5. —Let H be the centre of hand-rail and baluster; 
on A as centre describe the centre line of rail H, E, N ; make H B, B M and M N tangents to 
the centre line of hand-rail. Space the balusters around the centre line of rail and on the 
winders and steps below as required. Parallel to H B draw A F and M L indefinitely ; parallel 
to A B from 0, the centre of baluster, draw 0 S ; prolong M B to J indefinitely ; parallel to B J 
draw S G indefinitely; parallel to M L from the centre of balusters Q and C draw Q K and 
C D indefinitely. Further heights and inclinations to complete this drawing will be obtained 
after Fig. 2 , the elevation, is set up. 

Fig. 2 . Elevation of Tread and Rise as Figured, and as Taken from Fig. i, the 
Plan.—This elevation is set up for the purpose of finding heights and inclinations over the 
plan tangents H B, B E and E M of Fig. i ; also through the development of the centre line 
H G D K L to find the exact relation of the wreath-piece to the steps and rises, and by this 
means be enabled to get the lengths of balusters wherever placed on the centre line of rail, 
around the plan of cylinder. The elevation is necessary, too, to make the curve and fix the 
length and joints of the ramp ; also to get the odd lengths of balusters that may occur 
under the ramp as shown. In practice, the drawing of this elevation, and of such elevations 
generally, may be done full size, if desired, very conveniently by the use of the pitch-board, 
laying its hypothenuse along the edge of a drawing-board ; and for the winders transferring 
the tread and rise lines from the pitch-board by the use of a long parallel straight-edge. 

The treads around the cylinder must be measured on the centre line of rail as follows, at 

the plan Fig. i : From H to 1, the first tread in the cylinder, take its measure in two equal 

parts, and the second step from 1 to 2 into two parts : then 2 N of the remainder of the 

centre line is on the line of the floor. After completing the elevation anywhere along the line 
marked chord-line, set off H B, 3 ^^", equal to H B of Fig. i. Through B draw B J indefi¬ 
nitely and parallel to T H ; at any point along the line B J set off J E equal to B E of Fig. i. 

Through E draw E F parallel to B J ; at any point along the line E F set off F M equal to 

E M of Fig. I ; through M draw the line M L indefinite!)' ; from the floor-line to L set up 
5 ^"; then L becomes a fixed point from which the line L R may be drawn, R being the 
centre line of ramp; R may be raised or lowered to suit, but there can be no change at L. 
Wherever the line L R cuts the lines T H, B J, E F and M L, as at H, J and F, draw the lines 

H B, J E and F M parallel to the lines of tread. *At Fig. i make B J, E F and M L each 

equal B J of Fig. 2. As the heights are alike, connect J H, F B and L E of the last-mentioned 

figure. Place the baluster at 0 the same distance from the chord-line as at HO of Fig. i, 

and the other two balusters as at 1C and 2 Q, as marked alike at Figs, i and 2. Through 

0, C and Q draw 0 G, C D and P K parallel to the rises; make S G, C D and P K equal the 

heights indicated by the same letters at Fig. i. Through H G D K L trace the centre line of 

wreath ; parallel to this centre line trace the top and bottom lines of the wreath as shown 

by the short dash-lines. Place the centres of balusters that occur under the ramp as at 
the plan, and draw the dotted lines parallel to the risers ; then, to fijid the letigth of atiy of 
the balusters around the wreath or under the ramp; take for example C 4 of the wreath, which 

is 2I", add this to 2 '. 2 ", the usual height of balusters at X, X, then the baluster at C will be 

2 '. 4 J" at its centre line from the top of step to the under side of the hand-rail or wreath. 

Fig. 3 . Plan of Hand-rail from the Quarter-circle H E, Fig. i.—Make the heights and 
angles B J H and E F B agree with the corresponding letters at Fig. i ; draw A B ; from T 
parallel to A B draw T U ; parallel to B J draw 0 G ; through E draw H Z indefinitely; on 
B as centre with B F as radius describe the arc F Z. To find the angle with which to square 

the wreath-piece at both joints, prolong B E to R indefinitely; make E R equal E K; connect 

R A ; then the bevel at R will give the angle sought. 

Fig. 4 . Face-mould from Plan Fig. 3 .—On a line Z Z, make V Z, V Z each equal V Z of 

Fig. 3. At right angles to Z Z draw V M ; make V M equal V B of Fig. 3 ; connect M Z, M Z 

and prolong M Z to A; make Z A equal H R of Fig. 2 ; make M G, M G each equal J G of 

Fig. 3 ; through G and G parallel to V M draw U T, U T ; make G U, G U each equal 0 U of 

Fig. 3 ; make G T, G T each equal 0 T of Fig. 3 ; make V S equal V S of Fig. 3 ; through 
Z and Z draw T F, T F ; make Z F, Z F equal Z T, Z T ; make T B parallel to M Z ; make F 0 

and T D parallel to M A ; make the joints A and Z at right angles to the tangents. Through 

F U M U F of the convex and T S T of the concave trace the edges of the face-mould. The 
squaring of the wreath-piece at both joints is shown through the use of the bevel R, R 
taken from R of Fig. 3. 

Fig. 5. Plan of Hand-rail from the Quarter-circle E N, the Tangents E M and N M of 
Fig. I. —Make the angle M L E equal that given at M L E of Fig. i ; parallel to M L draw 
U 0 and V Q. 

Fig. 6. Face-mould from Plan Fig. 5, also Showing the Squaring of the Wreath- 
piece at Both Joints. —Draw the lines M F and M X at right angles ; make M N equal M N 

of Fig. 5 ; make the straight wood N X from 2 " up, at pleasure. At right angles to X M 

through X and N draw Z U and D E ; make M 0 Q F equal L 0 Q E of Fig. 5 . Through 0 , Q 
and F parallel to X M draw W Y, V C and E S ; make F Y, F W equal E Y, E W of Fig. 5 ; 

make Q C and Q V equal R C and R V of Fig. 5 ; make 0 S equal Z S of Fig. 5 ; make N Z 

equal N U ; make Z D parallel to N X. Through Y C S M Z of the convex and W V U of the 
concave trace the edges of the face-mould. The bevel L used to square the wreath-piece at 
the joint X is from L of Fig. 5 . The case of face-7nould Fig. 4 is treated in detail at Plate 
No. II, and face-77iould Fig. 6 is likewise treated at Plate No. 10. The development of the 
centre line of the wreath H G D K L of Fig. 2 is illustrated and explained in detail at Plate 
No. 20, Figs, i and 2. Sliding face-moulds to plumb the sides of wreath-pieces, also direc¬ 
tions for the application of bevels to square wreath-pieces, is given at Plate No. 56 . 


Plate No. 25 . 


















































































PLATE 26. 

Fig. I. Plan of the Top Portion of a Staircase Turning One Quarter to the Landing 
with Diminished Steps Around the Cylinder, Curved Rises, and Platform as given at 
Plate No. 5, Fig. 6.—This is an improved plan of stairs turning one quarter without the 
winders as by the old method given at Pl.\te No. 25, but the treatment of the hand-rail is 
precisely the same as that at the last-mentioned Plate, because the conditions around the 
cylinder are alike ; so that if the explanation is not given in this case with quite as much 
detail as before, it is for the reasons stated. It would be well to make a careful study of 
the preceding Plate in connection with this. Let F C A be the centre line of hand-rail and 
F D C, C B A the tangents. Place the balusters around the centre line of hand-rail as shown. 
Prolong F D to G indefinitely, and prolong K C to J indefinitely ; also D B to N. Connect 
K B ; from L parallel to K B draw L 0 ; from 0 parallel to B N draw 0 M indefinitely; from 
E parallel to F G draw E H indefinitely. The necessary heights and inclinations to complete 
this drawing will be established by drawing the elevation, and proceeding as directed at 
Fig. 2. 

Fig. 2. Elevation of Treads and Rises as Figured and as Taken from Fig. i, the 
Plan.—From the chord-line, which is the commencement of the cylinder, the treads are to be 
measured on the centre line of rail, from A to Z in two parts, and from Z to Q in two 
parts ; also on the line of floor Q F in two parts. Measuring the treads in two parts is done to get 
more exactly the stretch-out of the centre line. After drawing the elevation set off from the chord¬ 
line the length of tangent A B of Fig. i (which in this case is 3P') three times as shown, 
drawing lines at each of these distances parallel to the chord-line, to N J and G indefinitely ; 
make the height from the line of floor to G equal 5^": then G becornes a fixed point from 
which the line G R may be drawn, R being the centre line of ramp it may be raised or 
lowered to suit, but no change can be made at G without changing the usual length of bal¬ 
usters. Where the line G R cuts the lines I J, B N and the chord-line as at J, N and A, draw 

the lines A B. N I and J D parallel to the lines of tread. At Fig. i make B N, C J and D G 

each equal B N of Fig. 2, and connect G C, J B and N A. Place the centre of balusters L, F 

and E as on the plan L C and E Fig. i, mea5,uring from each riser on the centre line 
except the first baluster, wliich is measured from A, the chord, to L, the centre of baluster; 
parallel to the rise lines through E, F and L draw P H, F B and L M indefinitely; make P H 
equal P H of Fig. i; make C B equal C J of Fig. i ; make 0 M equal 0 M of Fig. i; then 

through G H B M A trace the centre line of wreath ; * parallel to this centre line set off and trace 

the top and bottom lines of the wreath as shown by the dotted lines. 

To Find the Length of any Baluster around the Wreath, take for Example:—F K, 
W'hich is 2 >¥ > ^dd this to 2'.2" the height of balusters at X X : then the baluster at F will be 
2'.5^" at its centre line from the top of step to the under side of the wreath. 

Fig. 3. Plan of Hand-rail from the Quarter-circle C F, the Tangents C D and F D of 
Fig. I.—Make the angle D G C equal the angle D G C of Fig. i. From R and S parallel to 
F G draw R Y and S X. 

Fig. 4. Face-mould from Plan Fig. 3, also Showing the Squaring of the Wreath- 
piece at Both Joints.f—Draw the lines C G and G B at right angles ; let G F equal D F of 
Fig. 3 ; F B the straight wood added should never be less than 2"; through F and B 

parallel to G C draw R A and D C indefinitely ; make G Y X C equal G Y X C of Fig. 3; through 

C at right angles to G C draw Z I ; through Y and X parallel to F G draw D V and S W 

indefinitely ; make F A equal F R ; draw A C parallel to F B ; let Y V, X W and C I equal U V, 

T W and C I of Fig. 3 ; let X S and C Z equal T S and C Z of Fig. 3. Through A G V W I of 

the convex and R S Z of the concave trace the edges of the face-mould. The bevel G of Fig. 3 

is used to square the w'reath-piece at the joint B as shown. The dotted lines show the least 
wood required to form the wreath-piece. 

Fig. 5. Plan of Hand-rail from the Quarter-circle AC, Tangents CB and A B of 

Fig. I. —Let the angles C J B and B N A each equal B N A of Fig. i. Connect P B ; from S 

draw S V parallel to P B ; from U draw U T parallel to BN; through A C draw A L indefi¬ 

nitely : on B as centre with B J as radius describe the arc J L. 

To Find the Angle with which to Square the Wreath-piece at Both Joints:—Prolong 
B C to Q indefinitely; on C as centre with C W as radius describe the arc W Q; connect Q P: 
then the bevel Q will give the angle required. 

Fig. 6. Face-rnould from Plan| Fig. 5, also Showing the Squaring of the Wreath- 
piece at Both Joints.—Let C J and C A each equal M L of Fig. 5. Draw C N at right 

angles to A J ; make C N equal M B of Fig. 5 ; connect N J and N A ; prolong N A to R indefi¬ 
nitely ; make A R equal A R of Fig. 2 ; make the joints R and J at right angles to the tangents ; 

let C Y equal M R of Fig. 5; make T 0 , T X and T 0 , T X both equal U V and U S ; through J 

draw X Z, make J Z equal J X ; through A draw X Z ; make A Z equal A X ; parallel to A R draw 

Z W and X S ; parallel to N J draw X F ; through Z 0 N 0 Z of the convex and X Y X of the con¬ 
cave trace the edges of the face-mould. The bevel Q used to square the wreath-piece at the 
joints J and R is taken from Q of Fig. 5. 


* The development of the centre line of a wreath, as in this case, is illustrated and explained in detail at Plate 20, 
Figs, i and 2. 

Sliding face-moulds to plumb the sides of wreath-pieces, also directions for the application of bevels to square 
wreath-pieces, are given at Plate No. 56. 

+ The face-mould Fig. 4 is explained in detail at Plate No. io. 

4 Face-mould Flc. 6 is explained in detail at Pl.\te No. ii. 




P L ATE N O. 26 . 








































































PLATE 27. 

Fig. I. Plan of the Bottom or Starting Portion of a Staircase Winding One Quarter, 
Similar to Plan Fig. I of Plate No. 4. —Let A C F be the centre line of rail around the 
cylinder, and A B, B D and D F tangents. Prolong F A to Q indefinitely; prolong A B to N and 
H C to T indefinitely. Space the balusters on the centre line as sliown. Further heights and 
inclinations necessary to complete this drawing will be obtained as directed from the elevation 
Fig. 2, when that drawing is completed. 

Fig. 2. Elevation of Tread and Rises as Figured and as Taken from Fig. i, the 
Plan. —Besides finding lieiglits and inclinations over tangents, tliis elevation is also set up to 
develop the centre line of wreatli DULPQ in its e.xact relation to the step and rise, thus 
giving the lengtiis of balusters under the wreath. The treads in the cylinder must be measured 
around the centre line of rail, and each tread taken in two parts in order to get more exactly 
the stretch-out of the circular line. After completing the elevation, anywhere along the line 
marked chord-line,—which is the commencement of the cylinder,—set off H A or A B of Fig. i 
(eitlier of wliich is 5^*') three times, drawing lines parallel to the chord-line indefinitely as shown. 
Let X X at the centres of the short balusters be the bottom line of rail; draw R N, the centre 
line, indefinitely and parallel to X X; at the intersection, N, draw N A at right angles to the 
chord-line; make Q R. 3", for straight wood to be added to that end of wreath-piece. Make 
E D, 5:1^"; connect D N; at T and D draw the lines D C and T B parallel to the treads. At 
Fig. I make CT and B N each equal CT and B N of Fig. 2; let A Q equal A Q of Fig. 2; 
connect Q B, N C and T D; make B 0 equal A Q; parallel to B C draw 0 M; parallel to B 0 
draw M G; connect G H, the level line common to both planes; parallel to G H draw J K and 
S R; parallel to A Q draw R P; parallel to T C draw K L and Z U. At Fig. 2 the centre of 

balusters EZJ and S are placed on each tread as at the plan, and the lines S P, J L and VZU 

are drawn indefinitely and parallel to the rise-lines; make V U and K L equal V U and K L of 
Fig. i; make G P equal R P of Fig. i; through tlie points DULPQ trace the centre line of 

wreath; the dotted lines are the top and bottom "of wreath set off from the centre line. D H 

is straight wood that will be added to that end of the lower wreath-piece. 

To Find the Lengths of Balusters Around the Wreath: —Take for example the baluster 
at S; S F is 5^", which, added to the usual height of balusters at X X, 2.2", makes the height 
of this baluster on its centre line from the top of step to under-side of wreath 2'.7^". 

Fig. 3. Plan of Hand-rail from the Quarter-circle F C of Fig. i with the Tangents 

F D and D C. —Make CTD equal CT D of Fig. i; parallel to F D draw P B and Q A. 

Fig. 4. Face-mould from Plan Fig. 3; also Showing the Squaring of the Wreath- 
piece at Both Joints. —Maxe the lines ND and Dl at right angles; let DBAN equal DBAT 
of Fig. 3; let D F equal D F of Fig. 3, and F I equal D H of Fig. 2; parallel to N D through 

F and 1 draw K M and J L; through B, A and N draw R L, 0 H and E G parallel to D F; make 

D J, B R, A 0 , N E and N G each equal D J, K R, X 0 and C E of Fig. 3; make A H equal X Q 

of Fig. 3; make F K equal F M; make K J parallel to FI; through M H G of the concave and 

KJ ROE of the convex trace the edges of the face-mould. The bevel at T used to square the 

wreath-piece at joint I is taken fro}n~^ ofYio,. 3. The dotted lines show the width of wood required 

to work out the wreath-piece. This face-mould is explained in detail at Plate No. 10. 

Fig. 5. Plan of Hand-rail from the Quarter-circle A C of Fig. i with the Tangents 
A B and C B.—The angles of inclination B NC and AQ B are taken from Fig. i. Make B 0 
equal A Q; make 0 6 parallel to B C, and 6S parallel to 0 B; connect S H, the level line common 
to both planes. Parallel to S H draw Y R, 5 L, B G, T U and AV; parallel to B 0 draw 4 M 
and R P; parallel to A Q draw UW; at right angles to H S draw AE indefinitely; draw C K at 
right angles to H S; on B as centre with N C as radius describe an arc at K; again on B as 
centre with B Q as radius describe the arc QE; connect E K. 

To Find the Angles with which to Square the Wreath-piece: —Prolong B A to F 
indefinitely and AH to J indefinitely; make A F equal A D; connect F G: then the bevel at F 
will square the wreath-piece over the joint A. Make H J equal SX; connect J C: then the bevel 
at J will square the wreath-piece over the joint C. 

Fig. 6. Face-mould from Plan Fig. 5; also Showing the Squaring of the Wreath- 
piece at Both Joints. —Draw the line K Q; let ZQ and ZK equal ZE and Z K of Fig. 5. On Z 
as centre with Z B of Fig. 5 as radius describe an arc at B; make Q B equal Q B of Fig. 5. and 
K B equal C N of Fig. 5: connect K B, B Q and BZ; make BW equal B W of Fig. 5: make 
B M 6 P equal N M 6 P of Fig. 5; parallel to Z B draw Q V, M L 5 , 6, 3 , 1 and P Y: make Q V and 
WT equal AV and U T of Fig. 5; make Z 2 , M L and M 5 equal Z 2 , 4 , 5 and 4 L of Fig. 5; make 
6, 3 , 6, 1 ,PY equal S I, S 3 and R Y of Fig. 5; through Q draw the line T C; make Q C equal QT; 
ihi'ough K draw the line Y A; make KA equal KY; parallel to B E draw TD indetinitelv; make 
Q E equal Q R of Fig. 2. The joints E and K are made at right angles to the tangents. Through 
A 3 L 2 VC of the convex and YI 5 T of the concave trace the edges of the face-mould. The slide¬ 
line is drawn at right angles to B Z. The dotted lines show the least width of wood required to 
work out the wreath-piece. This face-mould is explained in detail at Plate No. 12. The 
development of the centre line of this case of wreath is given in detail at Plate No. 20, Figs. 

3 and 4. Sliding face-moulds to plumb the sides of wreath-pieces, also direction for the application 
of bevels to square wreath-pieces, is given at Plate No. 56. 


Plate No. 27 . 













































































PLATE 2 8. 

Fig. I. Plan of the Top Portion of a Winding Staircase Making a Half-turn with 
a lo" Cylinder as given at Plate No. 6, Fig. 2.—Let A C B be the centre line of rail around 
the plan of cylinder, and A E, E D and D B tangents. Prolong E D to T indefinitely ; prolong 
F C to J. A E to L, and F A to R, all indefinitely. Space the balusters on the centre line as 
shown. Further heights and inclination of tangents to be shown in connection with this plan, 
including measurements that are necessary to develop the centre line of wreath and at the 
same time fix the lengths of balusters, will be obtained after drawing the elevation. 

Fig. 2. Elevation of Treads and Rises as Figured and as Taken from Fig. i, the 
Plan. —The treads in the cylinder must be measured around the centre line of rail, and each 
tread taken in two parts to get a nearer stretch-out of the circular line. Draw the centre 

line of level rail 5^^^ above the floor. To fix heights and inclination of tangents, try a straight¬ 

edge in determining W and B, points on the upper and lower chord-lines ; the points W and B 
are not fixed, but may be raised or lowered along the chord-lines at pleasure, taking notice, how¬ 
ever, that if B is raised it will increase the length of ramp ; also if W is raised the line R 0 will 
be shortened, a reasonable length of which is required to form the level easing as shown. At B 
draw B Y at right angles to the chord; set off four times 5I", the lengths of the tangents 
B D, D C, C E and E A of Fig. i. Through each of these points of division draw lines parallel 
to the rises ; from W parallel to the line of floor draw W R ; connect R B and prolong to 0 , 
and B to F indefinitely. Where the line R B cuts the vertical lines at T, J and L, draw the 
lines T C, J E and L A at right angles to the rise-lines. Let B F at the ramp and the same 
distance R E at the level easement be the allowance for straight wood to be left on those 

ends of the wreath. At Fig. i make D T, C J, E L and A R each equal D T of Fig. 2. Con¬ 

nect T B, J D, L C and R E. 

To Prepare for and Develop the Centre Line of Wreath. —At Fig. i draw G N and S P 
parallel to F E ; parallel to A B draw 2 H and P Q ; parallel to C J draw*Z K and N M. At 
Fig. 2 place the centres of balusters 5 , 4 U G S on the treads as at the plan, and through 
each of these centres draw lines parallel to the rise-lines indefinitely ; at baluster 5 make 

2 H equal 2 H of Fig. i ; at baluster 4 make 8, 6 equal D T of Fig. i ; at baluster U make 

Z K equal Z K of Fig. i ; at baluster G make N M equal N M of Fig. i ; at baluster S make 

P Q equal P Q of Fig. i. Through B H 6 K M Q W trace the centre line of wreath. The 

dotted lines are the top and bottom of the wreath set off from the centre line. 

To Find the Lengths of Balusters Around the Wreath: —Take for example the baluster 
at U. U V is iL', which added to the usual height of baluster at X, 2'.2", makes the height 
of this baluster on its centre line from the top of step to under side of wreath 2'.3^". 

Fig. 3. Plan of Hand-rail from the Quarter-circle B C of Fig. i with the Tangents B D 
and D C.—Let the angles D T B and C J D equal the same at Fig. i ; connect F D ; parallel 

to F D draw N R ; parallel to C J draw V L; through B and C draw B P indefinitely ; on D 

as centre with D J as radius describe the arc J P. 

To Find the Angle with which to Square the Wreath-piece at Both Joints Prolong 
DC to Y ; make C Y equal C W ; connect Y F: then the bevel at Y will give the angle required. 

Fig. 4. Face-mould from Plan Fig. 3; also Showing the Squaring of the Wreath- 
piece at Both Joints. —Let Z P, Z P each equal Z P of Fig. 3 ; make Z D at right angles 
to Z P and equal to Z D of Fig. 3 ; connect D P and D P ; make D L, D L each equal D L 

of Fig. 3. Through L and L draw N R, N R parallel to Z D ; make L R and L N each equal 

V R and V N ; make Z 0 and Z S equal Z 0 and Z S of Fig. 3 ; through P and P draw N H, 
N H ; make P H and P H each equal P N ; prolong DP to F ; make P F equal B F or RE 
of Fig. 2. The joints F and P are made at right angles to the tangents. Make N A and N A 
each parallel to the tangents. Through H R D R H of the convex and N S A of the concave 
trace the edges of the face-mould. The bevel at Y and Y, used to square the wreath-piece 
at both joints as shown, is taken from Y of Fig. 3. One face-mould (Fig. 4) in this case 
answers for both wreath-pieces. The joint F joins the ramp at F, and the same joint joins 
E, the level easement at the top. This face-mould is explained in detail at Plate No. ii. 
The development of the centre line of wreath is explained in detail at Plate No. 20, Figs. 

I and 2, by repeating the first quarter A C, Fig. i, and the development A E of Fig. 2 of that 
Plate. Sliding face-vioidds and squaring wreath-pieces are given at Plate No. 56. 



































































PLATE 29. 

Fig. I. Plan of the Bottom or Starting Portion of a Winding Staircase making 
a Half-turn with a lo" Cylinder as given at Fig. 2, Plate No. 6. —As this case is the same 

as the one already given at Plate No. 28 with the.exception of position, that being the top and 

this the bottom of a flight exactly alike in plan, there seems to be no need of repeating 
what has just been given in minute detail; but the plan, the elevation, etc., serve a most useful 
purpose in showing at a glance such differences as are naturally caused by the changed position 

of the same plan: such as the length of ramp (which at the bottom of a flight is shorter); 

also the lengths of balusters if required. But there need be no change of face-mould if care 
is taken in keeping the inclination of tangents alike. It will be seen upon examination that 
all measurements required at Fig. 2 are taken from Fig. i, or the reverse ; those measurements 
taken from Fig. 2 as required at Fig. i are lettered or figured alike. The lettering likewise 
agrees between the quarter B C of Fig. i and the plan of hand-rail Fig. 3. Also as far as 
possible the lettering is alike between the plan of hand-rail Fig. 3 and the measurements to 
be taken in connection with it for drawing the face-mould and squaring the wreath-piece at 
Fig. 4. 


Plate No. 29. 




































































PLATE 30. 

Staircases are frequently planned of greater width at the starting by curving the front 
string out, embracing in the curve from one to five treads; the least curve including but one 
step is done merely to save the width of staiis at this point by setting the newel-post a few 

inches aside. The larger curves including more steps give the stairs an inviting and more 

ornamental appearance. There is also a more recent practice of setting the newel on top of 
the first step by extending this step and riser in a curve sufficient to include the curve-out 
and the base of the newel as shown at Fig. 3. This gives in very little space a neat and 
elegant finish at the starting of a staircase. 

Fig. I. Plan of Curve-out in One Tread, together with Sufficient Elevation for 
those Measurements Required to Fix the Height of Newel and Draw the Face-mould 

or Parallel Pattern. —Let the bottom of rail rest on the centres of the short balusters at XX; 

"make R T equal 6", and T L half the thickness of rail; let L N be the centre line of rail; 

draw L M at right angles to the rise-line; parallel to the rise-line draw L A: then A at the 

plan on the centre-line of rail C A becomes a fixed point from which the tangent A B may 

be drawn at pleasure. Make C F equal M N; connect F A; from any point on the centre curve 

S draw a line parallel to A B touching the line C A at Z; draw Z 0 parallel to C F; at right 
angles to A B draw C D indefinitely; on A as centre with A F as radius describe the arc F D; 
connect D B. 

To Find the Angle with which to Square the Wreath-piece at the Joint over B:— 

Parallel to A B draw C K indefinitely; at right angles to A B draw B J; make J K equal C F; 

connect K B: then the bevel at K will give the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over C:— 
Prolong the tangent B A to G, and the tangent A C to H, indefinitely; make C H equal C E; 

connect H G: then the bevel at H will give the apgle required. 

Fig 2. Parallel Pattern for Wreath-piece from the Plan Fig. i.—Make AO VF equal 
the same letters at Fig. i. On F as centre with D B of Fig. i as radius describe an arc at B; 
on A as centre with A B of Fig. i as radius intersect the arc at B; connect B A; make B T 

equal B T of Fig. i; through T at right angles to A B draw Y Z; draw 0 S parallel to A B; 

make 0 S equal Z S of Fig. i. The width of the rail being 3", the parallel pattern will be 3!". 

Make V P and V Q each 1^"; parallel to V F draw P G and Q E; make B L and B W each ij"; 

parallel to B A draw LZ and W Y; on S as centre with ij" as radius describe a circle and 
sketch the curves P Z and Q Y touching the circle. The angle for squaring the wreath-piece at 

joint B is taken by the bevel K at Fig. i, and for the joint F the bevel H of Fig. i. 

Pig* 3 - Plan and Elevation of the Starting of a Staircase with the Front-string 
Curved Out and the Newel Set on Top of the First Step; the Elevation and Plan 
Prepared, Fixing the Height of Hand-rail at the Newel, and for Drawing the Face- 
mould. —Let the bottom of rail rest on X X, the centres of short balusters, and make A B, the 

centre line of rail, parallel to X X; make D E equal 8", and E F half the thickness of rail; draw 

F C parallel to the line of tread; draw A G parallel to the line of riser; then G becomes a 

fixed point on the line of tangent V G from which the level tangent G J Z must be drawn, 

but may be kept any distance from I to Z at pleasure. Parallel to Z G draw H 0 and L K; 
pandlel to V M draw 0 S and K W; from V at right angles to G J draw V N indefinitely; 
on G as centre with G M as radius describe the arc M N; connect N J. 

To Find the Angle with which to Square the Wreath-piece at the Joint over J:— 
From V parallel to G Z draw V R indefinitely; draw J T at right angles to J G; make T R 

equal V M; connect R J: then the bevel at R will give the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint overV:— 
Prolong Z G to U, and G V to P, indefinitely; make V P equal V Q; connect P U; then the 
bevel at P will give the angle required. 

Fig. 4. Parallel Pattern for Wreath-piece from the Plan Fig 3 —As this rail is to be 4" 
wide by 2^" thick, the pattern will ansvVer to get out the wreath-piece if 4^" wide. Draw the line 
G A; make G M equal G M of Fig. 3. Let M A equal 5" more or less for straight wood; on M as 
centre with N J of Fig. 3 ‘as radius describe an arc at J; on G as centre with G J of Fig. 3 
as radius intersect the arc at J; connect J G; make W L equal K L of Fig. 3; make S H equal 
0 H of Fig. 3. With 2%" radius describe circles from the centres J, H, L, M and A; connect B F 
and C E. The joints J and A are made at right angles to the tangents. Bend a flexible 
strip of wood touching the circles on the convex and concave and mark the curved edges 
of the pattern. The angle for squaring the wreath-piece at joint J is taken by the bevel at 
R of Fig. 3, and for the joint A by the bevel at P of Fig. 3. The height of hand-rail 
from the top of the second step, D, to the bottom of the rail, E, will equal—by adding the 
height of short baluster at X, which is 2'.2\ to the 8'^ raised between D and E—2'.io''. Face- 
mould for Figs, i or 3 is treated in detail by Plate No. 13. One feature of this plan given at 
Fig. 3 which is open to objectioii is the mcreased height of newel; how to reduce this, if required, will 
be shown by the following Plate, No. 31. 


Plate No . 30. 



1 



















































































PLATE 31. 

Fig. I. Plan and Elevation of the Starting of a Staircase with the Front-string 
Curved Out and the Newel Set on Top of the First Step, the Elevation and Plan Pre¬ 
pared to Continue the Hand-rail on a Common Inclination to the Newel, and for a Face- 
mould as Required. —Let the bottom of the rail rest on X X the centres of short balusters ; 
draw the centre line of rail Z R parallel to X X; make the tangents C V and V P of equal 

lengths; from V parallel to the rise-line draw V 5 ; parallel to the tread-line draw 5 Y; make 

4 R equal V P; through R parallel to V 4 draw W 8; at R draw R 4 at right angles to V 4 ; 

draw R U at right angles to R 5 ; make C G equal Y Z; connect G V; make V B equal 4 , 5 and 

at right angles to V P; connect B P; through C draw P D indefinitely; on V as centre with 
V G as radius describe the arc G D; at right angles to D P, through V draw Q 0 , F N M and 
T L; at right angles to C V draw A K and L J. 

To Find the Angle with which to Square Both Ends of the Wreath-piece: —Parallel to 

CV draw K I; at right angles to G V draw I H; prolong C V to E indefinitely; make CE 

equal I H ; connect E F, then the bevel at E will give the angle required. 

Fig. 2. Face mould from Plan, Fig. i; also Squaring the Wreath-piece at Both Joints. 

—Draw the line D D; make S D, S D each equal S D of Fig, i; at right angles to D D through 

5 draw Q 0 ; make S V equal S V of Fig. i; connect V D and V.D; make V K J and V K J 

each equal V K J of Fig. i. At right angles to D D through J K and J K draw T J, N M, 

N M and T J; make J T and J T each equal L T of Fig. i; make K M, K N and K M, K N each 

equal A M and A N of Fig. i; make S 0 and S Q equal S 0 and S Q of Fig. i; through D 
draw T Z at both ends; make D Z and D Z each equal T D. The lower end of the wreath- 
piece requires an addition of straight wood to fill out the plumb joint as shown at 6 U of 
the elevation, Fig. i. Make D F equal 6 U of Fig. i; make D U equal 4", more or less for 

straight wood; parallel to V U draw Z B and T A. The joints U and F are made at right 

angles to the tangents. Through Z M 0 M Z of the convex and T N Q N T of the concave 
trace the curved edges of the face-mould. The angle for squaring the wreath-piece at joints 
F and U is taken by the bevel at E, Fig. i. This case of face-mould is treated in detail at 
Plate No. 15. The difference in height between this manner of treating the hand-rail , and 
that of Fig. 3, Plate 30, is from the top of thfe rail at 8, where it joins the newel in that 

case, to the top of the rail at 2, where it joins the newel in this case, just 6 ". When the rail 

is set up at X X, 2'.2", the height of rail from W to 2 will be 26'.^', and between those 
points at Fig. 3, Plate 30, the height is 3'.^". Much more than 6 " can be gained if desired 
by moving the centre of the newel further towards the first riser on the line 3 , 3 and increas¬ 
ing tlie radius of the curve-out to suit the change. This might be very desirable in case of 

designing with this style of finish a low newel. 

Fig. 3. Plan of a Quarter-platform Stairs with a Quarter-cylinder of 8" Radius, the 
Risers each Set at A and B, the Chord-lines. —Let A Z B be the centre line of rail on the 

plan; divide the quarter-circle A B at Z in exactly two equal parts ; connect 6 Z ; at right angles 

to 6 B draw B E indefinitely; through A at right angles to 6 A draw THY indefinitely; through 
Z at right angles to 6 Z draw H E; make A Y equal 9", one tread; at right angles to A Y 
draw Y P; make Y P equal 8"—the rise; connect P A; parallel to Y P draw H K; parallel 

to AY draw K L; make L M equal Y L; divide PM in two equal parts at N; make H J 

equal M N; draw J W parallel to Y A; draw W X parallel to 5 A; from A draw A R parallel 
to the tangent H Z; make A R equal the tangent H Z; connect X R, which is the level 
line. Through H draw 5 G parallel to X R; anywhere on the centre curve-line draw the line 2 U 
parallel to X R; from A at right angles to X R draw A Q indefinitely; on the dividing radial 

6 D make Z D equal M N; connect D H; from Z at right angles to H G draw Z I indefinitely; 
on H as centre with H D as radius describe an arc cutting the line Z I at C; on H again 
as centre with K A as radius describe an arc cutting the line A Q at Q; connect Q C. 

To Find the Angle with which to Square the Wreath-piece at the Joint over Z :— 
Make Z F equal Z 0 ; connect F G; then the bevel at F will give the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A: 

—Make A T equal H V; connect T 5 ; then the bevel at T will give the angle required. 

Fig. 4. Parallel Pattern for Wreath-piece from the Plan Fig. 3. —Draw tlie line Q C, 
and make Q 4 C equal the same at Fig. 3. On Q as centre with A K of Fig. 3 describe an 

arc at K; on C as centre, with D H of Fig. 3 as radius, intersect the arc at K; also 4 K 

will equal 4 H of Fig. 3. Connect Q K, K C and 4 K; make K 3 equal H 3 of Fig. 3; make 

Q V equal A V of Fig. 3; draw V 2 parallel to K 4 ; make V 2 equal U T of Fig. 3; make Q B 

equal 3", or more for straight wood. The size of this rail is to be 2^" thick by 3" wide, 
therefore the parallel pattern will require to be 3I" wide. With if "' as radius on C, 3 , 2 , 
Q, B as centres, describe circles. Make a line touch these circles for the concave and convex 
edges of the pattern. The joints B and C are made at right angles to the tangents. Tne 
angle for squaring the wreath-piece at joint C is taken by the bevel at F of Fig. 3, and for 
the joint B by the bevel at T of Fig. 3. The slide line is drawn at right angles to the 
level line 4 K. This pattern serves for both wreath-pieces, C being the centre joint. A face- 
mould of this kind is treated in detail at Plate No. 16. This quarter-cylinder with its con¬ 
necting steps and risers should be planned in such a way that the quarter-wreath could be 
got out in one piece of a common inclination as shown at Plate No, 37, Figs. 5, 6 and 7. 
It would cost less and be a superior-shaped wreath-piece. 


Plate No. 31. 




Rise 

























































PLATE 32. 


Fig. I. Plan of Hand-rail composed of Two Curves of Different Radius as a Curve- 
out at the Starting of a Staircase, taken from the Plan given at Fig. 5, Plate No. 6.— 

This shape of curve is a necessity in order to make a proper connection with a square newel 

where the sides of the newel are required to be set parallel to the sides of the hallway, as 

shown by the plan above mentioned. An elevation has to be set up in order to fix the lenp^th 
of plan tangent D F, as at AC of Fig. 2 . And the greater the required height of newel the 

higiier up the line A C must be placed, and therefore the shorter this line and the plan tangent 

will be. 

Fig. 2. Elevation of Tread and Rise as at Plan of Hand-rail Fig. i, taken from 
Fig. 5 of Plate No. 6. —Let the bottom line of rail pass througli X X, the centres of the short 
balusters of the regular tread; make LQ 5 ^", more or less, depending on what height of newel 
is demanded; make QV half the thickness of rail; draw VGA parallel to the line of treads; 
let C B be the centre line of rail parallel to XX. When the hand-rail is set’up, the height from 
the top of the first step, L, to the bottom of the rail, Q, will be 2 '. 2 ^ at X and 5 ^" more at L 0, 

equal to 2 '.’]V. At Fig. i maxe D E equal A B of Fig. 2; connect EF; parallel to D E draw H T, 

1 U, J V, K W and LY. 

Fig. 3. Face-mould to be taken from Plan Fig. i; also Squaring the Wreath-piece 
at Both Joints. —Make FTUVWYE equal the same at Fig. i; draw FG at right angles toFE; 
make FG equal FG of Fig. i; tlirougli G parallel to FE draw AH; parallel to F G draw T H, 

U 1, VJ, W K, 0 L and N M; make G A equal G H. Set off all measurements from the line FE as 

taken on the line F D of Fig. i according to the eorresponding letters at the curves. Through 
NOXXXXXA of the convex and M LKJ IH of the concave trace the curved edges of the face- 
mould. The bevel at E of Fig. i is used to square the wreath-joint G of Fig. 3. It would be 
well to add about 3" for straight wood to joint E. 

Fig. 4. Plan of the Starting Portion of a Staircase with the Front-string Curved 
Out, and Embracing Four Treads of Equal Widths at the Wall-string and Front¬ 
string. —At the elevation. Fig. 5, the bottom line of rail rests at X X, the centres of short 
balusters; BC and DC are the centre lines of rail. Fixing the point C controls the height 
of rail at the newel; also the length of tangent A C at Fig. 4. FE being 9", add that to the 

lieight of sliort baluster at X, 2 '. 2 ", and the sum 2 '.ii" will be the height between F and E. 

In a flat curve like this it is desirable to keep the point C up as high as can be allowed, for 
it shortens the tangent AC, Fig. 4, and makes the bevel line CO more nearly a tangent. Let 
the angle ABC equal the same at the elevation; connect CO; parallel to C 0 draw 4 W, IV, 
Q U, R G, 8 K and AM; parallel to A B draw J H, S V, U Z, 3Y and 8 X. From A draw A 9 at 

l ight angles to 0 C; on C as centre with C B as radius describe the arc B 9; connect 9 0. 

To Find the Angle with which to Square the Wreath-piece over the Joint A:— 
Draw S 6 parallel to C B; prolong CA to L; make AL equal A 6 ; connect LG: then the bevel 
at L will give the angle sought. 

To Find the Angle with which to Square the Wreath-piece over the Joint 0 :— 

Make 2M equal AB; connect MO: then the bevel at M will give the angle sought. 

Fig. 6. Face-mould from Plan Fig. 4; also Squaring the Wreath-piece at Both 

Joints. —Let 0 B equal 0 9 of Fig. 4 . On B as centre with B C of Fig. 4 as radius describe 

an arc at C; on 0 with 0 C of Fig. 4 as radius describe an intersecting arc at C; connect 0 C 

and C B; make the spaces lettered on B C agree with those of B C at Fig. 4 ; parallel to 0 C 

diaw XJ, Y I, Z Q, VTR and H W: take all measurements on the tangent AC, Fig. 4 , and set 
them off from the line B C as shown by the corresponding letters; make ON equal OJ; through 
B draw WK; make BK equal B W; prolong C B to A; make B A 4 " for straight wood. The 
joints A and 0 are at right angles to the tangents. Through WT5FEPN of^ the convex and 
KRQIJ of the concave trace the curved edges of the face-mould. The angle for squaring the 
wreath-piece at joint 0 is taken by the bevel M at Fig. 4 , and tliat for joint A by the bevel L 
at Fig. 4 . Face-mould Fig. 3 is treated in detail at Plate No. 10, and face-mould Fig. 6 is 
treated likewise at Plate No. 13. 


Note. —The line O C of Figs. 4 and 6 is not a tangent, but is simply a level line used to fix the height, control the 
joint, and to guide the measure, or drawing, of the face-mould. Care should be taken in laving out the squaring at joint O 
of the wreath-piece that the width of rail be made equal to iW of FiG. 4, because, although J N is at right angles to O C, it 
is oblique to the curve, and mav, therefore, measure a quarter of an inch or more over the width of rail. After the wreath- 
piece is squared at the joint O, a portion of the wood, equal to N U J of Fig. 4, is cut away to correct that joint. 



Plate No. 32. 























































































PLATE 33. 

Fig. I. Plan of the Landing Portion of a Straight Flight of Stairs with the 
Top Riser Set in the Whole Depth of a Ten-inch Cylinder, thereby Saving Five 
Inches Space. —The plan made as described with the addition of the plan and centre 
line of rail, p7‘oceed to set up the elevatioji, Fig. 2, resting the bottom line of rail on 
the centres X X of the short balusters, and the centre of rail A D in position parallel to 
X X, the point D being fixed by the level line G D, and its height F G from the floor. 
The point A is decided by the position of the chord-line as taken from the plan ; A C is 
drawn parallel to the line of tread. This completes the preparation of the elevation, all being 
obtained that is required in fixing the point A and D together with the height C D. Again 
at Fig. i, parallel to the line of string, let the line F A pass through C, the centre of rail ; 

make CD at right angles to C A, and C D A equal to C D A of Fig. 2. From A draw the 

line A I touching the centre line of rail at Q ; the exact place of Q is determined by draw¬ 
ing a line from the centre 0 , at right angles to A Q; parallel to A Q draw R Y, S X, V W H J 

and P U; parallel to C D draw T 2 , N M, X 3 and Y Z ; from C at right angles to A Q draw 

C E; on A as centre describe the arc D E; connect E Q. 

To Find the Angle with which to Square the Wreath-piece at the Joint over Q:— 

Anywhere along the line W J draw H 1 parallel to 0 Q. Make H J equal N M; connect J I; 

then the bevel at J will give the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over C:— 

From M parallel to A C draw M K; make C F equal K L; connect F G; then the bevel at F 

will give the angle required. 

Fig. 3. Face-mould from Plan Fig. i, also showing the Squaring of the Wreath- 

piece at Both Joints. — Draw the line D Q indefinitely ; make D Q equal E Q of Fig. i. 

On D as centre, with DA of Fig. i as radius, describe an arc at A; and on Q as centre, with 
Q A of Fig. i as radius, intersect the arc at A. Connect A Q and A D; prolong A D to L and 
equal to A E of Fig. 2, or at pleasure for straight wood. Make D 2 M 3 Z the same as at 
the corresponding letters of Fig. i. Parallel to A Q draw Z R, 3 S, M V W and 2 U P; through 

Q draw R C at right angles to A Q; make Q C equal Q R; make A 4 ‘equal A 4 of Fig. i ; 

make 3 , 5 S equal X 5 S of Fig. i; make M V, M W equal N V, N W of Fig. i; make 2 U, 2 P 

equal T U,T P of Fig. i; through D draw P B; make D B equal D P; parallel to D L draw 

P E and B F; through C 4 5 V U B of the convex and R S W P of the concave trace the edges 
of the face-mould. The tangent Q A being a level line, the face-mould slides along the joint 
C. The angle with which to square the wreath-piece at joint Q is taken by the bevel at J of 

Fig. I, and for the joint L is taken by the bevel at F of Fig. i. This face-tnould is treated in 

detail at Plate No. 14. The level portion of rail Q B may have as much straight wood attached 
to B as seems desirable. 

Fig. 4. Plan of the Starting Portion of the Same Flight of Stairs given at 
Pig. I with a Ten-inch Cylinder, and the Starting Riser Set in the Whole 
Radius or Depth of Cylinder, Saving Another Five Inches. —Having made the plan 
as described, proceed to set up the elevation. Fig. 5. Let the bottom line of rail rest 
on the centres X X of the short balusters. Place the centre of the rail C B in position par¬ 
allel to X X, the point C being fixed by the level line G C, and its height F G from the 
floor. The point B is fixed by the position of the chord line as taken from the plan. A C G 
is drawn parallel to the line of floor. The place of B, the height A B, and the distance A C 
is all that is required of the elevation. Again at Fig. 4 prolong the diameter-line S A of the 
cylinder to B indefinitely; at the centre line of the rail A, at right angles to A B, draw A C; 
make ABC equal to A B C of Fig. 5. From C draw the line C D tangent to the centre line of 
the rail at the point D, to be determined by drawing a line from 0 at right tingles to the 
tangent C D. The remaining portion of the rail D S is level, and at S straight wood can be 
added at pleasure. To draw the face-mould proceed as at Figs, i and 3. It is necessary to 
give further attention to this case of hand-rail from the fact that although the riser is set 
in the cylinder the same at the bottom as at tlie top of the flight, there is a difference 
requiring another face-mould unless it is thought worth while to make the top face-mould answer 
also for the bottom. In the latter case let C stand exectly as it is, and make C L equal 
C A of Fig. i and L N equal C D of Fig. i; then change the place of the chord-line—or 
commencement of the cylinder—to L, and describe the centre line of the rail from the new 
centre, and draw from C a new tangent, and the case will then agree with the top plan 
tangents and face-mould. 

Fig. 6. Elevation Same as Fig. 5, for the Development of the Centre Line of Wreath 
from Plan, Fig. 4. — The corresponding letters and figures of Figs. 4 and 6 will give a 
snfficient explanation. This development of the centre line of the wreath-piece is introduced 
to demonstrate the correctness of treating such cases in the manner here shown. Treating 
cases of hand-railing like this in two quarters — the joint in the centre—makes it necessary to 
square up both pieces and draw two face-moulds, with no better result and nearly double the 
cost. This face-mould. Fig. 3, is treated in detail at Plate No. 14. The development of the 
centre line of wreath is given in detail at Plate No. 21, Figs, i and 2. 




Plate No. 33, 












































































PLATE 34. 

Fig. I. Plan of the Top Portion of a Straight Flight of Stairs with a Seven-inch 
Cylinder, the Landing Riser set in the Whole Depth of the Cylinder. —This plan is 
introduced for the purpose of showing; how to draw a face-mould and work a wreath, taking 
the whole cylinder in one piece. Having made the plan as shown and described, proceed to 
set up an elevation of tread and rises, as at Fig. 2. Let the bottom line of rail rest on XX, 
the centres of the short balusters, and place the centre line of rail A E in position parallel 
to X X; the point E is fixed by the level line E G and its height F G from the floor. The 
point A is fixed by the position of the chord-line as taken from the plan. A B is drawn 
parallel to the line of the floor. The points A and E being determined together with the 
height B E, that is all that is required of the elevation. 

Fig. 3. Plan of Rail with its Centre Line as given at Fig. i, to be Prepared for 
Drawing a Face-mould by which to get out in One Piece a Wreath for the Whole 
Cylinder; also Showing howto Construct a Paper Representation of a Solid, which 
Objectively Exhibits the Principles involved in this Case of Face-mould. —Draw A B at 
right angles to A Q; make ABE equal ABE of Fig. 2. From B draw the line B P, touching 
the centre line of rail; from D at right angles to B P draw DC; parallel to B 0 draw Q U, 
OS, 2, 5, D J Z and H X7; parallel to B E draw U V, S T, 5, 6 , J 1 and X I. 

To Find the Angle with which to Square the Wreath at the Joint over A:—From D 

draw D F at right angles to A D; make D F equal J K; connect F A: then the bevel at F will 

give the angle sought. The joint of the wreath over Q will require some over-wood and will 
also have to be cut plumb. 

To Find the Angle with which to Cut the Joint of the Wreath over Q Plumb:— 
On B as centre describe an arc touching the line E A, and at 10 connect 10 A: then the bevel 
at 10 will give the required angle. 

To Find the Amount of Over-wood required in Making the Joint of Wreath over 

Q Plumb: —Make 22, 24 equal two inches, which is half the thickness of rail plank; draw 

22, 24 at right angles to 10, A: then 10, 22 will be the extent of over-wood. 

To Find the Angle with which to Square the Wreath at the Plumbed Joint over 
Q:—At P draw P N at right angles to PA; make P N equal B E; connect N A: then the 
bevel at N will give the angle sought. 

To Find the Slide Distance, or Movement of Face-mould, to Plumb the Sides of 
the Wreath :—Prolong P B to Y indefinitely; frorq A draw A W indefinitely and parallel to 
P B; anywhere above E draw 12, W at right angles to Y B; make 12, Y equal B E; connect 

Y W; make 11,4 at right angles to Y W and equal to two inches, half the thickness of plank; 

then 11, Y is the slide distance. 

The Paper Representation of a Solid is bounded on its base by the lines A B P A; the 
vertical side B P is formed by raising the perpendiculars B 16 and P 15, each to equal B E; 
connect 16, 15. 

To Develop the Cutting Plane; —On 15 as centre with N A as radius describe an arc at 

18, and on 16 as centre with A E as radius intersect the arc at 18; connect 15,18 and 16, 18, 

Cut through the paper the outlines A E B 16, 18, 1 5 P N A; then with a sharp-pointed instrument 
scratch the base-lines A B P A, and the level line 16, 15; touch the cut edges with glue and 
fold them in place with the faces turned so that all the lines are on the outside. 

Fig. 4. Face-mould for the Whole Cylinder from the Plan Fig. 3. —Draw the line 
G C equal to G C of Fig. 3 . On G as centre, with A E of Fig. 3 as radius, describe an arc 

at E, and on C as centre, with C B of Fig. 3 as radius, intersect the arc at E; connect E C and EG; 

prolong E G to P indefinitely; make G I J 6 TV equal A I 1 6 TV of Fig. 3 ; parallel to E C draw 

V Q, T 0, 6 , 3, 2, J Z Z and 1 H 7; make E 8 equal B 8 of Fig. 3 ; make V U Q equal U R Q of 

Fig. 3 ; make TO equal SO of Fig. 3 ; make 6 , 3, 2 equal 5,3, 2 of Fig. 3 ; make J Z, J Z equal 
J Z, J Z of Fig. 3 ; make 1,7 and I H equal X7 and X H of Fig. 3 ; through G Q draw A B; make 

G B equal G H; parallel to G P draw FI F and B Y; draw F Y at right angles to G P; make 

C R equal 0 C; make Q A equal Q 2; through AR8UZ7B of the convex and 2, 0 3 Z FI of 

the concave trace the edges of the face-mould. Through C at right angles to C E draw the 

slide line R P. G P for straight wood equals A P of Fig. 2 , but need not be in any case more 

than two or three inches. In laying out the wreath add to the joint 2 A over-wood equal to 

10, 22 of Fig. 3 , which is required to plumb the joint as shown at Fig. 6 . 

Fig. 5. Squaring the Wreath. —The angle for squaring the wreath at the lower joint F 
is taken by the bevel F at Fig. 3 . The face mould is moved along the slide-line 11, K from 
11 to Y, equal to 11,Y of Fig. 3 . The position is shown by the dotted lines. The upper or 
level joint has to be cut plumb along the line 2 A in the direction Q B, as shown at Fig. 6 , 

by the use of the bevel 10 of Fig. 3 . QG B equals 10 ZW of Fig. 6 . The sliding of the 

face-mould will give the plumb-joint if wood enough is left on. After cutting the joint plumb 
it is laid out for squaring by the bevel N, taken from N of Fig. 3 , the plumb-line N C passing 
through the centre G; but as the plane of the plank brings the centre G too low by the 
distance M L of Fig. 3 , the centre G has to be raised that much, to FI, and if the wood proves 
scant on the top for the form of rail, glue on the piece cut off at the bottom. 

Finally, the case here presented is left to the decision of intelligent mechanics as to its 
economy and value in practice. My own opinion is that for small-sized moulded rails and 
cylinders not over eight inches, with proper management and use of the band-saw, it will effect 
a considerable saving. For instance, after the level joint is made plumb by the use of the 
bevel 10 , or by sliding the face-mould as directed, and the squaring lines are marked on both 
joints, with the band-saw cut off the level slab J X X; rest J X X on the saw-table, and the 
wreath will be in position to cut the sides plumb. If,desirable a slab may also be sawed off 
the lower end along the line Z Z and on the angle Z Z, as shown at Fig. 2, When the sides 
of the wreath are sawed plumb, lay the convex side on the saw-table and saw the top and 
bottom, rolling the wreath on the table as required; cut with care, and at first a little at a 
time. Practice will soon make it easy to cut the wreatli comparatively perfect, ready to bolt 
to the adjoining straight, with little cutting and shaping to do by hand. A good way to test 
this case would be to get it out of soft wood as a trials either half or full size, as convenient. 


Plate Mo.34. 



Scale IVzIn. = 1 Ft. 






































































PLATE 35 


Fig. I. Plan of the Top Portion of a Straight Flight of Stairs with a Seven-inch 
Cylinder, the Landing Riser set at the Chord-line or Commencement of the Cylinder.— 
A second way of drawing a face-mould and working a wreath for the cylinder in one piece. 

This method, as compared with that given at Plate 34 , will at least have the merit of 

greater simplicity. After drawing the plan as shown and described, set up the tread and 
rise as at Fig. 2 . Rest the bottom of the rail at X X, the centres of the short balusters. The 
bottom of the level rail B is set up four inches as usual. Draw D B parallel to the floor line; 
let B H equal the thickness of rail; make H K parallel to B D; at E draw E F indefinitely 
and at right angles to X X; at G draw G K parallel to the riser. At right angles to A B 
of Fig. I draw B 2, 0 H. S Y, E X, P G and A Z, all indefinitely; draw H K of Fig. 2 to Y of 
Fig. i; parallel to Y K draw D of Fig. 2 . At Fig. i make FZ the thickness of rail and draw 

Z X parallel to F D; touching the angles D and C draw the line 4, 6 ; parallel to D C and 

touching the angles Y and Z draw L 2; at right angles to L 2 draw lines touching W. N, X 
and F; then these square sections show the plank canted in position, with the joints and the 
wreath as it is to be first sawed out. Make 2 J equal C D of Fig. i; parallel to L 2 draw J 5; 
at right angles to L 2 draw 2 J, H M, G 8 , Z 5, etc., measuring all the points for tracing the 
edges of the face-mould from the line A B, and setting them off from the line J 5; as I M 
equals 0 Q, K 8 equals P R, etc. , 

To Find the Angle for the Joint E G of the Wreath, Fig. 2, to be Applied from the 
Face of the Plank along the Line 4 U of Fig. i:— From V of Fig, i draw a line to K of Fig. 2 . 
parallel to N D; from U of Fig. i draw a line to J of Fig. 2 , parallel to V K; at Fig. 2 , 
parallel to the rise-line, draw J K; make VT of Fig. i equal F K of Fig. 2 ; connect T U; 
then the bevel at U will give the angle required. The application of the bevel U for the 
joint along 4 U is shown at Fig. 3 . In marking out the wreath it would be better to leave 
a half-inch more wood at the concave,—in fact, a little more wood, both thickness and 
width, would be well, for this wreath is forced at the lower joint, and although its shape 
would be passable, it could be much improved with more wood. After preparing the lower 
joint with the bevel U, and facing the upper joint on the line Y 2, square from the face of 
the plank. Lay out the squaring of the upper joint with the bevel H as seen; then sliding 
the face-mould will give the plumb sides at the lower end. Cut off the slab W Y at right 

angles to the joint, and resting the cut portion on the saw-table,* with a suitable block tacked 

temporarily to the under side of the end thrown up to keep it in position, saw the two sides 
plumb; then rolling the wreath on the convex side, saw the top and bottom to the required 

shape. Some of the slab cut off at the bottom may have to be glued on at the top, depend¬ 

ing on the shape and thickness of the rail. 

WAINSCOT. 

Fig. 4. Vertical Cross-section of Hall Wainscot, of which an Elevation of a Portion 
is made at Fig. 5, as it Appears along the Wall, in Connection with the Level Wainscot 
at the Starting of a Staircase. —In the best panel-work of hard wood, the frame is put 
together, the mouldings glued in place, and the whole finished and varnislied. Afterwards the 
varnished panels are set in from the back and fastened at X X with three-cornered pieces of 
stout sheet-metal driven in the frame; or in place of the metal strips of wood are nailed into 

the frame and against the panels at X X. As to the height, wainscot should be up the flight 

as compared with the height of the connecting level wainscot. There is no fixed rule; but as a 
basis, let A B of Fig. 5 , the level wainscot, be tliree feet in height as at Fig. 4 . Make a vertical 
line along any riser of the flight C D equal three feet; then if, after measuring on the line H J — 
which is drawn at right angles to the inclined string—the width of bottom rail E, middle rail F, 
and top rail G, as given at the section. Fig. 4 , the space left for panels is unpleasantly narrow, 

changes may be made and the height given at C D altered to suit. 


* The wreath may be placed in the position here referred to (after the sides have been sawed plumb and before the top 
is shaped), and the joint as at Fig, 3 tested by the pitch-board. 





Plate No. 35. 







Fig.3. 


FiG.1. 


Landing Ris e.r 



Floor 



% 


y 

Pi 

1 

1 


B 

1 


1 

1 







Scale IV2 In. =1 Ft. 


Floor 



Fig.4. 


Scale H In. = 1 Ft. 


























































































































































































































PLATE 36. 


Fig. I. Plan of a Winding Stairs Turning One Quarter at or about the Middle of the 
Flight. — This plan is given at Plate No. 5, Fig. ji. After making the plan, describe the 

centre line of the rail Q H, the plan tangents Q C and C H. Place the centres of balusters as 

required. Before the plan can be completely prepared to draw a parallel pattern or a face- 
mould, the elevation must be drawn. 

Fig. 2 . Elevation of Plan as given at Fig. i. —Set up tlie treads and rises as figured and 
given at the plan according to the scale. The treads in the cylinder must be measured on the 

centie line of the rail, and each tread taken in two parts for the purpose of getting more accu¬ 

rately the stretch-out of the centre line. Place the centres of balusters on each tread as shown 
on the plan, and except at the centres of the short balusteis 0 , draw lines parallel to tlie rise¬ 
lines, and indefinitely. At the upper portion of the elevation tlirough the centres of the short 
balusters 0 0 draw the bottom line of the rail, and place the centre line N C in position par¬ 
allel to 0 0, but indefinite in length. Anywhere along the upper chord-line set off the length 
of plan tangent H C of Fig. i, and draw the line C M parallel to the choid-line; and where the 
centre line N A intersects at C, draw the line C D at right angles to the chord-line. Anywhere 
along the lower chord-line P B set off the length of the plan tangent Q C of Fig. i and draw 
the line F E. E is a fixed point from which the line E L may be drawn to suit its position over 

the winders and the requirements of the ramp. Wherever the line E L intersects the chord¬ 

line P B as at B, draw the line B F at right angles to the chord-line. Make A J equal four 
inches for straight wood on the upper end of the wreath-piece; and make B G also four inches 
for straight wood on the lower end. The ramp is curved as shown. Again at Fig. r make 
C E :.t right angles to Q C and equal to F E cff Fig. 2 ; connect E Q; make H D at right 
angles to C H and equal to D A of Fig. 2; connect D C. 

To Find the Directing Level Line: —Make C G equal H D; make G F parallel to C Q, 
and F 0 paiaHel to C E; connect 0 N, which is the level line sought. Parallel to N 0 draw 
I Z, U 0, 2 T, C M and 3 W; parallel to C E draw T X and Z Y; parallel to H D draw V/ K; 

from H at right angles to NO di'aw H A indefinitely; fiom Q at right angles to N 0 draw 

Q B indefinitely: on C as centre with C D as radius describe the arc D A; again on C as 
centre wiili E Q as radius describe an arc at B; connect B A. ^ 

To Find the Angle with which to Square the Wreath-piece at its Joint over H:— 

Make H L equal H J; connect L M; then the bevel at L will give the angle required. 

To Find the Angle with which to Square the Wreath-piece at its Joint over Q:—Pro¬ 
long H N to R indefinitely; make N R equal 0 P; connect R Q; then the bevel at R will give tlie 
angle sought. 

To Develop the Centre Line of the Wreath-piece in Position over the Elevation, 
Fig. 2 .— Make Z Y, T X and W K equal the heights at the corresponding letters of Fig. i; then 
through B Y H K A trace the centre line of the wreath. Set off half the thickness of rail each 
side of the centre as shown by the dotted lines. 

To Find the Length of Balusters: —Take for example the one marked 3; 3 V measures 
5 ^'', which, added to 2 '. 2 ", the length of short baluster at 0 , equals between the top of 

the step 3 and the bottom of the rail V at the centre of the baluster. 

Fig. 3. Parallel Pattern for the Wreath-piece over the Plan, Fig. i.— Make the line 
B D equal B A of Fig. i; make D S equal A S of Fig, i; on D as centre with C D of Fig i as 
radius describe an arc at C; and on B as centre with Q E of Fig. i as radius intersect the arc 
at C; also on S as centre with S C of Fig. i as radius test the intersection of the arcs at C; con¬ 
nect D C, C B and S C; prolong C B to G and CD to J ; make B G equal B G of Fig. 2; make 
D J equal A J of Fig. 2 ; make B Y F X equal Q Y F X of Fig. i; make C K equal C K of Fig. t; 
parallel to the level line C S draw K 3, X 2, F U and Y I; make Y I, F U, X 2 and C V equal Z 1, 
0 U, T 2 and C V of Fig. i; make K 3 equal W 3 of Fig. i. The joints J and G are made at 
right angles to the tangents. 

At a trial—laying out the squaring of the wreath-piece at joint J with the bevel L of Fig. i, 
also joint G with bevel R of Fig. i — it is found that the position of the form of rail at 
joint J takes the greatest width of stuff, equal to 5 ", therefore, with 2 |" radius describe circles 
on the centres GB1 U2V3DJ, and trace lines touching the circles to complete the pattern. 

Develoinnent of the centre line of wreath-piece in cases of this kind is given in detail at 
Plate No. 20 by the quarter-circle Q V of Fig. 3. Face-mould and parallel pattern of this 
character is treated in detail at Plate No. 12. 


P LATE No. 36 . 

























































PLATE 37. 

Fig. I. Plan of a Half-turn Platform Stairs with the Opening between the Strings— 
Usually Built to Connect in the Form of a Semicircle—Composed of Two Quarter-circles 
with Straight between. —Plans of platform stairs differently treated are given at Plates 6 
and 7. The situation of the risers in connection with the chord lines is, in this case, determined 
by trial through the elevations of tread and rise set up at Figs. 2 and 3. 

Fig. 2. —Let the bottom line of hand-rail pass through X X, the centres of short balusters; 
the thickness of rail is set off parallel to X X by the line E D; the line C B is the centre of 
a four-inch plank, from which the wreath-piece is to be worked out. A J is four inches, which 

the rail is to rise above the floor more than the height to be raised at XX; J B is half the 

thickness of rail, and the height of B, touching the centre line C B, determines the exact 
position of B to the riser H; and at the plan Fig. i A H is made to equal A H of Fig. 2. 

This explanation and the corresponding letters tvill serve Fig. 3. At Fig. i, to prepare for drawing 

the face-mould, place the pitch-board as shown, marking the line of hypothenuse W M; prolong 
U A to M; parallel to U M draw T N and V 0. 

Fig. 4. Face-mould from Plan Fig. i; also the Squaring of Wreath-piece at Both 
Joints. —Draw U A and A K at right angles; make A I LU equal Al LU of Fig. i; make A N OW 
equal M N 0 W of Fig. i; make W K four inches for straight wood; through N, 0, W, K, parallel 
to U A, draw Y Z, IV, F E and B C; make W F and W E each equal the same at Fig i; make 

0 1 and 0 V equal P 1 and P V of Fig. i; make N Y equal S Y of Fig. i; parallel to W K 

draw F B and E C; make L J equal LT; parallel to L U draw J R; through U draw R Z 
parallel to AW; through F 1 Y 1 J of the convex and E V T of the concave trace the edges of 
the face-mould. The squaring of the centre joint U by the use of the pitch-board, as shown, 

is a sufficient explanation. At joint K the sides of the rail are at right angles to the plane 

of the plank; D H S S is the over-wood to be cut away at the bottom of the lower wreath- 
piece, and at the top of the upper one. 

Fig. 5. Plan, as given at Plate 5, Fig. 10, of a Quarter-platform Stairs turning 
One Quarter with a Quarter-cylinder. —Draw the plan of rail, also the centre line, and upon 
the latter space the balusters, as required. Make the tangents to the centre line of the rail, 
B F and B 0, and let the distance from the angle B, both ways to each riser, equal half a 
tread—from B to S and 4E from B to 1. By this arrangement there is between the two 
risers one tread, which brings the wreath-piece on a common inclination with the flight, and 

makes the best possible shape of it. To Arther prepare the plan for drawing the face-mould, 

place the tread of the pitch-board on the tangent B 0 and mark the line B Q; prolong the 

tangent OB to C; prolong A 0 to Q. A line connecting A B will be tlie level line. Parallel 

to A B draw R L and H G; parallel to 0 Q draw X N and 1 M; parallel to B C draw G E; 

from F through 0 draw F P; on B as centre with B Q for radius describe the arc Q P. 

To Find the Angle with which to Square Both Joints of the Wreath-piece: —On B 
as centre describe an arc touching the line C F and D; connect D F: then the bevel at D 
will give the angle required. 

Fig. 6. Elevation of Tread and Rise, including the Platform, as given at Plan and 
as Figured.— The platform is measured at the plan on the centre line in two parts from riser 
to riser. The heights and inclinations, the rail above and below, the joints Y and Y, are all 
shown in position; also the development of the centre line of wreath. The letters correspond 

with the plan Fig. 5 and with those at the joints of the face-mould. The length of baluster 

is here determined as before explained. 

Fig 7. Face-mould over Plan Fig. 5; also Showing the Squaring of the Wreath- 
piece at the Joints. —Draw the line P F indefinitely; make K P and K F each equal K P of 
Fig. 5; from K at right angles to F P draw K C; make K C equal K B of Fig. 5; connect 

C P and C F; prolong C F and CP to Y; make P Y and F Y equal the same at Fig. 6; make 

the joints Y, Y at right angles to the tangents; make F M and P M each equal Q M of Fig. 5; 
through M and M parallel to C K draw L R, L R; make M L and M R equal 1 L and 1 R of 
Fig. 5; make CZ equal B Z of Fig. 5; through F and through P draw R V; make FV equal 
F R, and P V equal P R; parallel to C Y draw V X and R X at each end; through V L Z L V of 
the convex and R K R of the concave trace the edges of the face-mould. The angle for 
squaring the wreath-piece at both joints is given by the bevel D, Fig. 5. The face-mould. 

Fig. 7, is treated in detail at Plate No. ii, and face mould, Fig. 4, is also treated in detail at 

Plate No. 10. 


I 



Plate No. 37. 








































































































PLATE 38. 


Fig. I. Plan of a Platform Stairs with the Risers at Platform set in the Whole 
Depth of the Cylinder. —Draw the centre line of rail and space the balusters as required, 
also draw 0 A and A Q, F G and G C tangents to the centre line of rail at each quarter- 
circle. To prepare the plan for measurements that will develop the centre line of wreath, or 
to draw the face-mould, the elevation must first be set np. 

Fig. 2. Elevation of Treads and Rises as given at the Plan and as Figured; also 
Development of the Centre Line of Wreath. —Let ilie bottom line of rail above and below 
the platform pass through X X, the centres of short balusters. Place the chord-lines—of which 
tliere are four—as given on the plan, Diaw the centre line of rail L B and G R parallel to 
X X; at light angles to the chord-line D 0 draw 0 A equal to the first tangent 0 A of Fig. i. 

Parallel to D 0 draw A B; at right angles to A B, touching B, draw QT; make QT equal the 

second tangent A Q of Fig. i; make C G at right angles to CM and equal to lUe tangent 
C G of Fig. i; and draw the line EZ parallel to J F; from Z draw the line Z T; where the 
inclined line Z T intersects the choid-line J F at F, draw F E at right angles to J F. Place the 
balusters numbered 1, 2, 3, 4, 5, 6 as on the plan, and draw a line through the place of each 
baluster parallel to the rise-line and indefinitely. 

To Prepare the Plan, Fig. i, for Finding the Lengths of Balusters: —Make C M G 
equal the same of Fig. 2; make G Z F equal E Z F of Fig. 2; make Q N A equal Q N T of 
Fig. 2; make ABO equal the same at Fig. 2; make AJ equal Q N; make J Y parallel to 

A 0, and Y 8 parallel to B A; connect 8 R; parallel to 8 R draw 2 V; parallel to Q N ciiavv 

V W; make M H equal G Z; draw H E parallel ^to C G, and E T parallel to C M; connect T S; 
parallel to S T draw 5 K and 4, 1; parallel to C M draw K U; parallel to G Z draw I P. The 

heights for the balusters are taken as numbered and lettered, and set up at the elevation, Fig. 2, 

as designated by the same numbers and letters; then through these letters—M U P F N W Y 0— 
trace the centre line of the wreath-pieces. Set off each side of the centre half the thickness of 
rail as shown by the dotted lines; next, to get the length of balusters: take for example baluster 
4— this measures from the platform to the bottom of the rail, 4f", which, added to 2 '. 2 "— the 
length of short balusters at X X—equals 2'.6f" from the top of the platform to the bottom of the 
wreath along the centre line of baluster. 

Fig. 3 . • Plan of the Lower Quarter Wreath-piece. —The heights A B and Q N are taken 
from those lettered the same at Fig. 2 . Make A F equal Q N; draw F E parallel to AO, and E D 

parallel to B A; connect C D, which is the directing level line; parallel to C D draw V W, A K, R S 

and Q Y; at right angles to the level line C D from 0 and Q draw 0 M; also Q P, each indefi¬ 
nitely. On A as centre with B 0 as radius describe an arc at M; again on A as centre with A N 
as radius describe the arc N P, connect P M. 

To Find the Angle with which to Square the Wreath-piece at the Joint over 0 :— 

Prolong Q C to H; make C H equal D I; connect H 0; then the bevel at H will give the angle 

required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over Q:— 

Prolong A Q to L; make Q L equal Q 8 ; connect L K; then the bevel at L contains the angle 

sought. 

Fig. 4. Face-mould taken from Plan of Quarter-circle Fig. 3, also Showing the 
Squaring of the Wreath-piece at Both Joints. —Make 0 N J equal M J P of Fig. 3 . On N 
as centre with N A as radius describe an arc at B; on 0 as centre with 0 B of Fig. 3 as radius 
describe an intersecting arc at B; on J as centre test the intersection at B with J A of Fig. 3 
as radius;* connect N B. 0 B and J B; prolong 0 L equal to 0 L of Fig. 2; and prolong B N 

equal to N S of Fig. 2 . Make N T equal N T of Fig. 3 ; make 0 X E equal 0 X E of Fig, 3 ; 

parallel to the level line J B draw N Y, T R , E G U and X V; make N Y equal Q Y of Fig. 3; 

make T R and B 7 Z equal S R and A 7 Z of Fig. 3 ; make E G, E U equal D G, D U of Fig. 3 ; 

make X V equal W V of Fig. 3 ; through N draw R F; make N F equal N R; make the joints S and 

L at right angles to the tangents; from R and F draw lines to the joint parallel to N S; thiough 0 

draw V D; make 0 D equal 0 V; through F Y 7 G D of the convex and R Z U V of the concave 

trace the curved edges of the face-mould. The slide-line is made at right angles to the level 

line J B. The angle for squaring the wreath-piece at joint L is taken by the bevel at H of 

Fig 3 , and that for the centre joint S is taken by the bevel at L of Fig. 3. This face-mould 

is treated in detail at Plate No. 12 . The development of the centre line of wreath-piece in 

a case of this kind is shown in detail at Plate No. 20 , plan of quarter-circle R Q V, and 

Fig. 4, Q to Y. 


* Instead of using the length of the level line J A of Fig. 3, as at J B of Fig. 4, as a test, it may be used in any 
case, together with the length of either one of the tangents, to establish the angle of tangents as at B. 


I 




































































PLATE 39. 

Fig. I. Plan of Stairs with Two Connecting Platforms Divided by a Riser, set in 
the Ce'ntre of the Cylinder in a Direction Parallel to the Strings; also with the Risers 
Landing on and Starting from the Platforms, Each set into the Cylinder Three 
Inches.* —Set off the centre line of rail and space the balusters as required; also draw the 
tangents D C, C 1 and A F, F H to the centre line of the rail at each quarter-circle; then to 
find the angles of inclination for the tangents it is necessary first to set up the elevation. 

Fig. 2. Elevation of Treads and Risers as given at the Plan and as Figured; 
also the Development of the Centre Line of Wreath-pieces. —Let the bottom lines of rail 
above and below the platforms pass through X X, the centres of short balusters. Place the 
chord-lines, of which there are four, as given on the plan; draw the centre line of rail R E 
and T G parallel to X X; at right angles to the first chord-line W D draw D C equal to the 
first tangent D C of Fig. i; parallel to W D draw C E; touching E, at right angles to 2 B, 
draw M Q equal to the second tangent 2 C of P'ig. i: then Q becomes a fixed point. At 
the uppermost chord draw FI G at the intersection of the centre line G T, equal to the fourth 
tangent FI F of Fig. i; from the third chord-line, Y A, make A F equal F A of Fig. i; make 

F N parallel to Y A: then N becomes the next higher fixed point. Connect the two fixed 

points N and Q; where the inclined line N Q intersects the chord-line at A draw A F at right 
angles to Y A; divide the straight between the two quarters B A in two equal parts at S: 

tlien S will be at the centre joint of wreath-pieces. Place the balusters numbered 1, 2, 3, 4. 5 

as on the plan, and draw a line through the place of each baluster parallel to the rise-lines 
indefinitely. 

To Prepare the Plan Fig. i for Finding the Length of Balusters: —As the angles 
of inclination in this case happen to be all alike, the angle DEC of Fig. 2 may be set in 

place over each tangent, as D E C, C B 2, A N F and H J F; connect Q F, also G C. From the 

centre of baluster 5 draw 5 M parallel to FI J; from the centre of baluster 4 draw 4 K parallel 
to Q F; parallel to F N draw K L; parallel to G C from the centre of baluster 1 draw 1, 0; 
parallel to C E draw OP; at Fig. 2 make 0 P equal 0 P of Fig. i; make K L and U V of 

Fig. 2 equal K L and 5 M of Fig. i; then through D P B, A L VJ of Fig. 2 trace the centre 

line of wreath-pieces; set off each side of the centre line half the thickness of rail as shown 
by the dotted lines. 

To Find the Lengths of Balusters: —Take for example No. 2 baluster, where 2Z equals 
4 T', which added to 2 '. 2 \ the length of short balusters at X X, makes the length of that 
baluster on the line of its centre from the top of step to the bottom of rail 2'.6Y- 

Fig. 3. Plan of the Lower Quarter-circle with Tangents and Angles of Inclination 
Lettered Alike and as taken from Fig. I.—From K draw K M parallel to G C; from L draw 
L H parallel to 2 B; through D and 2 draw DA indefinitely; on C as centre with C B as radius 
describe the arc B A. 

To Find the Angle with which to Square the Wreath-piece at Both Joints:— 
Prolong C 2 to F indefinitely; on 2 as centre describe an arc touching the inclined line C B and 
at F; connect FG: then the bevel at F contains the angle required. 

Fig. 4. Face-mould from Plan Fig. 3 ; also Squaring of the Wreath-piece at Both 
Joints. —Draw the line A A indefinitely; let J A and J A each equal J A of Fig. 3 ; make J C at 
right angles to J A and equal to J C of Fig. 3 ; connect CA and C A; prolong C A to S and C A 

to R, each indefinitely; make C FI and C FI each equal C FI of Fig. 3; make AR equal D R or 

J T of Fig. 2 , for straight wood; make AS equal B S or A S of Fig. 2 , this being one half the 
straight between the quarter-circles of which this cylinder is composed; through FI and FI 
parallel to the level line JC draw M K, M K; make FI K and FI M equal LK and L M of Fig. 3; 
make J ! and J N each equal J I and J N of Fig. 3 ; through A at both ends draw K W; make 

A W, A W each equal A K; the joints S and R are made at right angles to the tangents; from 

K and W draw lines parallel to the tangents, touching the joints; through W M C M W of the 
convex and K N K of the concave trace the curved edges of the face-mould The angle with 
which to square the wreath piece at the centre joint S and joint R is contained in the bevel 
at F of Fig. 3 . The development of the centre line is explained in detail at Plate No. 20 , 
Fig. I, quarter-circle A C, and A Y E of Fig. 2 . This case of face-mould. Fig. 4, is given in 
detail at Plate No. ii. This plan of stairs is given at Plate No. 7, Fig. 2 . 


* A riser is calculated as set in a cylinder three inches more or less from the chord-line to the face of the regular 
tread, and not from the chord-line to any point of the cylinder to which the riser may be curved. 


















Plate N? 39. 











































































PLATE 40. 

Fig. I. Plan of Half-turn Platform Stairs with 15" Cylinder, the Risers Landing on 
and Starting from the Platform set in the Cylinder yi", its Whole Depth.— This plan is 
given at Plate No. 7 , Fig, i. Describe the centre line of rail, and draw the tangents A E, 
E X. Space the balusters as required. Before proceeding further in the preparation of this plan 

for drawing the required face-mould it is necessary to set up the elevation. 

Fig. 2. Elevation of Tread and Rise as given at the Plan and as Figured. —Place 
the chord-lines, of which there are two, in position as shown on the plan Fig. i. Let the 

bottom line of rail pass through the centres of short balusters at 0 0 , and draw the centre 

line of rail D C and G K each parallel to 0 0. From the first chord-line A make A E equal 

A E of Fig. i; parallel to a rise-line draw E C; at A draw A E at right angles to the chord¬ 
line; make J G equal A E; draw G X parallel to the rise-line; from G draw G J at right 

angles to G X; from C draw C X parallel to the line of platform; divide G X at F in two equal 

parts. 

To Prepare the Plan Fig. i as Required to Measure for Drawing a Face-mould.— 

Prolong X E to N and to C; make E C equal E C of Fig. 2 ; connect C A; prolong J X to F 

and to I; make X F equal X F of Fig. 2 ; connect F E; make E D equal X F; draw D B parallel 

to E A; make B K parallel to EC; connect K J, which is the level line; parallel to J K draw 

Y 2; parallel to J A draw 2 W; parallel to J K draw E M, U V and X S; parallel to J X draw 

V R; at right angles to J X draw A H and X Z, both indefinitely; on E as centre with E F as 
radius describe the arc F Z; again, on E as centre with C A as radius describe an arc at H; 
connect H Z. 

To Find the Angle with which to Square the Wreath-piece at the Joint over X;— 
Make X N equal X G; connect N M: then the bevel at N will contain the angle required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A;— 

Make J I equal K Q; connect I A: then the bevel at I wTll contain the angle sought. 

Fig. 3. Face-mould from Plan Fig. i, also Showing the Squaring of the Wreath- 
piece at Both Joints. —Draw the line Z H; make Z 0 and 0 H equal the same at Fig. i; 
on Z as centre with F E of Fig. i as radius describe an arc at C; on H as centre with A C 
of Fig. I as radius intersect the arc at C; on 0 as centre with 0 E of Fig. i as radius test 
the intersection of the arcs at C; connect Z C, H C and 0 C; prolong C H 10 D; make H D 

equal D A or H K of Fig. 2 ; make the joints D and Z at right angles to the tangents; make 

H W B equal A W B of Fig. i; make C R equal E R of Fig. i; parallel to 0 C draw Z S. R U, 

and through B, L 4 and W Y; make W Y equal 2 Y of Fig. i; make B L and B 4 equal K L 

and K 4 of Fig. i; make C P equal E P of Fig. i; make R U equal V U of Fig. i; make 

Z S equal X S of Fig. i. Through H draw Y T; make H T equal Y H; through Z draw U J; 

make Z J equal Z U; draw lines from T and Y parallel to the tangent touching joint D. 
Through T L P S J of the convex and Y 4 0 U of the concave trace the curved edges of the 

face-mould. The slide-line is at right angles to the level line 0 C. The angle for squaring 

the joint Z is taken by the bevel N of Fig. i, and for squaring joint D by the bevel I of 
Fig. I. 

Fig. 4. Elevation of Step and Rises at the Starting, Set up for the Purpose of Find¬ 
ing what Position the Bottom Riser should take next to the Chord-line of the Cylinder 
when the Wreath-piece is Treated in the Simplest Manner, with the Over-wood all to be 
Removed from the Top. —Let the bottom line of rail pass through the centres of short bal¬ 
usters X X. Set off the thickness of rail X E, and draw E H parallel to X X; let X D be the 

thickness of plank, out of which the wreath-piece is to be worked. Make the line A F pass 

through the centre of X D and parallel to XX; make B C four inches and C A half the thickness 

of rail. The intersection of the line A J at its given height with the centre line F A at A fixes A 

as the centre of the rail at the centre of the plank, and the distance from A to the chord-line J 
must be 8|", equal to J A of Fig. i. 

Fig. 5. Plan of Cylinder Connecting Step and Hand-rail at the Bottom of this Flight 
of Stairs. —Let the chord line H of the cylinder be set at the same distance from the bottom 
riser as shown at the elevation Fig. 4. 

To Prepare the Plan for Drawing a Face-mould : —Draw the tangents H J and J K; 
from the centre D describe the plan of rail. Set the pitch-board with the tread on the line 
H J, and mark the pitch-line J Q; prolong D H to Q; parallel to K J draw L N, V 0 and U P 

Fig. 6. Face-mould from Plan Fig. 5, also Squaring the Wreath-piece at Both 
Joints. — Draw Y J, J K at right angles; make J N 0 P Q equal the same at Fig. 5 ; make J K 

equal J K of Fig. 5 . Through K parallel to J Y draw X L; through N 0 P Q Y draw lines 

parallel to J K indefinitely; make N M, 0 W, P S and Q equal Y M, X W, Z S and H R of Fig. 5 . 

Make 0 V, P U and Q T equal X V, Z U and H T of Fig. 5 ; draw lines from T and R to the 

joint Y parallel to Q Y; through X 1 M W S R of the convex and L V U T of the concave trace the 
curved edges of the face-mould. The wreath-piece at the joint K is squared by the use of the 
pitch-board as shown. The joint at Y is square, and E D is the over-wood as shown at E D 
of Fig. 4. Face-mould Fig. 6 is treated in detail at Plate No. 10. Face-mould Fig. 3 is explained 
in detail at Plate No. 12 . I'he development of the centre line at Fig. 2 of wreath-pieces is given 

in detail at Plate No. 20 , Fig. 3, quarter-circle Q V, and Fig. 4 , Q Y. 









Plate N° 40, 



Scale l^z In. = 1 Ft. 





















































































PLATE 41. 

Fig. I. Plan of Stairs with Two Quarter Platforms and a Tread between, All 
Connected with, and Dividing Equally, a lo" Cylinder. —This plan of stairs is given at 

Plate No. 5 , Fig. 9 . Describe the centre line of rail, and space the balusters as required. 

Draw the tangents A B, BE, EG and G J to the centre line of rail A E J To find the angles 

of inclination of these tangents, and other points of measurement by which to get the lengths 
of balusters, it is necessary to set up an elevation. 

Fig. 2. Elevation as given at Plan Fig. i and as Figured.— Measure the three treads 
in the cylinder on the centre line, and, as before explained, of treads situated in curves. Let 

the bottom line of rail pass through the centres of short balusters at X, 1 below and X X 

above; draw the centre line of rail LC parallel to X, 1, and the centre line F G parallel to 

X X; make A B and J G equal A B and J G of Fig. i. From A at right angles to the chord¬ 
line draw A B, and from G at right angles to the chord-line draw G J; from C at right 

angles to H E draw C E; divide E J at D in two equal parts. Place the centres of balusters 

1, 2, 3 as at the plan, and draw lines through each parallel to the rise-lines and indefinitely. 

At Fig. I, to further Prepare for the Development of the Centre Line of Wreath 
and for the Lengths of Balusters; —Make the angles A C B and J H G equal A C B and J H G 
of Fig. 2; prolong J G to F, and K E to D; make E D and G F each equal E D of Fig. 2; 

connect D B; connect F E; make G U equal J H; draw U X parallel to G E; make X W parallel 

to G F; connect W K, which is the directing level line for the quarter-circle E J; make D N 

equal B C; draw N L parallel to E B, and 4 . 0 parallel to E D; connect 0 K: then 0 K will 

be the directing level line for the quarter-circle A E; from the centre of baluster 1 draw 1 S 
parallel to K 0; parallel to B C draw ST; from the centre of baluster 2 draw 2 V parallel 

to K 0; make V M parallel to ED; through the centre of baluster 3 draw 3 Z parallel to KW; 

make Z Y parallel to G F. At Fig. 2 make ST equal S T of Fig. i, and V M equal V M of 

Fig. i; make ZY equal Z Y of Fig. i; through ATMYH trace the centre line of wreath, 
and set off each side of the centre half the thickness of rail as shown by the dotted lines. Of 
the three balusters around this cylinder, only one. No. 3 , will require a half inch more length 
than usual for short balusters. A L and H F are 4 " straight wood to be left on the wreath- 
pieces above and below the cylinder. 

Fig. 3. Plan of Rail and the Centre Line of the First Quarter AE with the Tangents 
A B and B E, and the Angles of Inclination A C B and B D E, from Fig. i.—Make D N equal 
BC; draw N L parallel to E B, and LO parallel to ED; connect 0 K, the directing level line; 

parallel to 0 K draw 4, I, B U, W X and AH; parallel to BC draw XG; parallel to DE draw 

Y M; at right angles to 0 K draw AQ indefinitely; and again at right angles to 0 K draw E R 
indefinitely; on B as centre with B D as radius describe the arc DR; on B again as centre with 
C A as radius describe an arc at Q; connect Q R. 

To Find the Angle with which to Square the Wreath-piece at the Joint over E;— 
Prolong BE to V; make EV equal N P; connect V K: then the bevel at V will contain the angle 
required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A:— 
At U draw U T at right angles to KA; make UT equal B F; connect T A; then the bevel at T 
will contain the angle sought. 

Fig. 4. Face-mould from Plan Fig. 3; also Squaring the Wreath-piece at Both 
Joints, —Draw the line Q R; make RS and SQ equal the same at Fig. 3 . On Q as centre with 
A C of Fig. 3 as radius describe an arc at B; on R as centre with D B of Fig. 3 as radius intersect 
the arc at B; from S test the intersections at B by S B of Fig. 3 ; connect R B, Q B and S B; 

prolong BQ to C; make QC equal A L of Fig. 2 ; make the joint C and R at right angles to 

the tangents; make QG equal A G of Fig. 3 ; make R M L equal D M L of Fig. 3 ; parallel to S B 

draw Q H, G W, L J and 4, I; make M I and M 4 equal Y I and Y 4 of Fig. 3 ; make L J and B Z Y 

equal 0 J and B Z Y of Fig. 3 ; make G W and Q H equal X W and A H of Fig. 3 ; through R 

draw 4P; make R P equal R 4; through Q draw W F; make Q F equal Q W; from F and W 

draw lines to joint C parallel to B C; through F H Z I P of the convex and W Y J 4 of the 

concave trace the curved edges of the face-mould. The slide-line is drawn at right angles to 

the level directing line S B. Joint R of the wreath-piece is squared by the bevel at V of 
Fig. 3 , and joint C by the bevel at T of Fig. 3 . The face-mould is explained in detail at Plate 
No. 12 . The development of the centre line of the wreath-piece is explained at Plate No. 20; 
the quarter-circle Q V of Fig. 3 , and Q Y of Fig. 4. 


Plate N? 41 . 


f 



i 






















































































PLATE 42. 

Figr. I. Plan of Landing and Starting Two Flights, Both in Connection with a I2" 
Cylinder. — This plan is given at Plate No, 6, Fig. 3. Tiie centre line of tlie rail may be 
described, the balusters spaced, and tlie tangents to tlie centre line drawn; then, to find the 
angle of inclination of these tangents, an elevation of the plan must be made. 

Fig. 2. Elevation of Plan as given at Fig. i and as Figured ; also Development 
of the Centre Line of Wreath. —In setting up the elevation, the treads in the cylinder must 
be measured between chord-lines on the centre line of rail, each in two parts, so as to get 
practically near enough to the stretch-out of the circle. Draw the chord-lines in the position 
given on" the plan, and parallel to the rise-lines. Place the centre of balusters as given on 
each step of the plan, and through these centres draw lines parallel to the rise-lines indefinitely. 
Let the bottom line of rail above and below each pass through the centres of short balusters 
X X; draw the centre line of lail at I G and T B each parallel to X X. Make the distance 

from the chord-line AW to BC equal the tangent A C of Fig. i; draw BC parallel to AW; 

at A draw A C at right angles to A W; make the distance from the chord-line J S to G equal 
the tangent H G of Fig. i; draw G F parallel to J S; at G draw G H at right angles to J S; 
from B draw B F parallel to the line of floor; divide G F in two equal parts at D; transfer 
the angle ABC to ABC of Fig. i. The three remaining tangents all happen in this case to 
have the same angles of inclination,* so that the angle H J G may be placed at E D C, G F E 
and H J G, Fig. i. Make D H of Fig. i equal C B; draw H J parallel to E C; make J V parallel 

to E D; connect V K, which is the directing level line for the quarter E A. The directing 

level line for the quarter E H—that quarter having a common angle of inclination—is a line 
drawn from G to K. From the centre of baluster 1 draw 1 L parallel to C B; from the centre 
of baluster 2, parallel to K V, draw 2, 0; parallel to E D draw 0 K and 3 M; from balusters 
4 and 5 draw 4 N and 5 Q parallel to K G; parallel to G F draw N P; parallel to H J draw 
Q R. At Fig. 2 make Z R over baluster 5 equal Q R of Fig. i. Make N P over baluster 4 
equal N P of Fig. i; make E M over baluster 3 equal 3 M of Fig i; make B 0 equal 0 K 
of Fig. i; parallel to B F draw 0 K; make V L over baluster 1 equal 1 L at Fig. i; through 
J R P M K L A trace the centre line of wreath; set off each side of the centre half the thickness 
of rail as shown by the dotted lines. 

To Find the Lengths of Balusters:— For example, take baluster 3; 3 U measures 6 f", 
which must be added to 2 '. 2 ", the length of short balusters X X, and this makes the length of 
that baluster, measured along its centre frorn top of step to under side of rail, 2 '. 8 f". 

Fig. 3. Plan of Rail for Quarter-circle, Centre Line A E, Fig. i, with Angles of 
Inclination—over Tangents— ABC and CDE; also the Directing Level Line VK as 
Transferred from Fig. I.—Parallel to K V draw Z 5, C Q and Y W; parallel to E D draw 4F; 
parallel to C B draw X N; at right angles to V K draw E T and A 0 indefinitely; on C as 
centre with C D as radius describe the arc DT; again on C as centre with B A as radius 
tlescribe an arc at 0; connect 0 T. 

To Find the Angle with which to Square the Wreath-piece at the Joint over E: — 

Prolong C E to S; make E S equal H G; connect S K: then the bevel at S contains the angle 

required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A:— 

From Q draw Q P at right angles to K A; make Q P equal C R; connect P A: then the bevel 

at P contains the angle sought. 

Fig. 4. Face-mould from Plan Fig. 3; also Showing the Squaring of Wreath-piece 
at Both Joints.— Draw the line A T indefinitely; make T U and U A equal T U and U 0 of 
Fig. 3 . On T as centre with C D of Fig. 3 as radius describe an arc at B; on A as centre with 
A B of Fig. 3 as radius intersect the arc at B; with U C of Fig. 3 test the intersection of the arcs 

at U B; connect T B, B A and U B; make B F equal C F of Fig. 3 ; make B N equal B N of Fig. 3 ; 

parallel to U B through F and N draw 5 Z and W Y; make F Z and F 5 equal 4 Z and 4, 5 of 

Fig. 3 ; make B I U equal C I U of Fig. 3 ; make N Y and N W equal X Y, X W of Fig. 3 ; through 

A drawYC; make AC equal AY; through T draw ZG; make TG equal T Z; make AJ for straight 
wood equal A T of Fig. 2; make the joints J and T at right angles to the tangents; from Y and C 
draw lines to joint J parallel to B J; through G 5 I W C of the convex and Z U Y of the concave 

trace the curved edges of the face-mould. The wreath-piece is squared at joint J by the bevel 

at P of Fig. 3 , and joint T is squared by the bevel at S of Fig. 3 . The slide-line is drawn at 

right angles to the level line U B. A face-mould of this kind is explained at Plate No. 12, 

and the development of the centre line of such a wreath-piece as this is given at Plate No. 20; 
quarter-circle Q V of Fig. 3 , and Q Y of Fig. 4 . 

Fig. 5. Plan of Rail for Quarter-circle E H of Fig. i, with Angles of Inclination over 
Tangents E F G and G J H, as Transferred from E H of Fig. i.— Connect G K; parallel to 
G K draw L Y; parallel to G F draw Z D; through H and E draw H W indefinitely; on G as centre 
with E F as radius describe an arc at W. 

To Find the Angle with which to Square the Wreath-piece at Both Joints Prolong 
G H to N; make H N equal H R; connect N K: then the bevel at N will contain the angle 
required. 

Fig. 6. Face-mould from Plan Fig. 5; also Showing the Squaring of the Wreath- 
piece at Both Joints.— Draw the line W. W; make S W, S W each equal S W of Fig. 5 ; draw 
SG at right angles to S W; make SG equal S G of Fig. 5 ; connect GW and GW; prolong 
G W to A; make W A for straight wood equal J I of Fig. 2 ; make the joints A and W at right 
angles to the tangents; make G D, G D each equal F D of Fig. 5 ; through D and D draw L Y and 
L Y parallel to G S; make D Y and D L at both sides of the centre each equal Z Y and Z L 
of Fig. 5 ; through W and W draw L M and L M; make W M equal W L; make G T equal 
G T of Fig. 5 ; througli M Y T Y M of the convex and L S L of the concave trace the curved 
edges of the face-mould; from L and M draw lirves to joint A parallel to G A. A face-mould 
of this kind is explained in detail at Plate No. ii, and the development of the centre line 
of wreath-piece at Plate No. 20 , Fig. i, quarter-circle A C, and Fig. 2, A E. 

* If the height G F had been more or less than twice the height HJ, then the fUce-nitnld for the quarter-circle H E would 
have been of the same kind as that of Fig. 4. 





Plate N° 42. 





































































PLATE 43. 

Fig. I. Plan of the Starting of a Staircase with One Parallel Step at the Centre of 
a 15" Cylinder, together with a Quarter Platform.— This plan is given at Plate No. 7, 
Fig. 9. The centre line of rail may be described, the tangents drawn, and the balusters 
spaced as required; but to find the angle of inclination over the plan tangents, etc., the ele¬ 
vation must first be set up. 

Fig. 2. Elevation of Treads and Rises as given at Plan Fig. i, and as Figured.— 

Let the bottom line of rail be drawn through the centres of short balusters X X, and draw the 

centre line of rail A N parallel to X X. Place the chord-line H J parallel to the rise-line, and 

in position as at the plan; make J G equal J F at Fig. i; draw F G parallel to the rise-line, 

and at the intersection G draw G J at right angles to the rise-lines. Make F D equal F E 
of Fig. i; draw E D parallel to the rise line; at the intersection D draw D F at right angles 
to the rise-line; make E C equal E C of Fig. i; make 1 B equal 1 B of Fig. i; draw B N at 
right angles to the line of floor; make B K equal 4 ", and K N half the thickness of rail; 
draw N E parallel to the floor-line. Place the centre of each baluster on the treads as num¬ 
bered, and as fixed around the centre line of rail at the plan, and draw lines through each 
parallel to the rise-lines indefinitely. At Fig. i make the angles of inclination J H F, F G E 

and E D C all equal J H G of Fig. 2 ; parallel to A D through the centre of baluster 2 draw N M; 

from the centre of baluster 1 draw 1 L parallel to A D; draw I K parallel to A D. Connect 
F A; from 3 parallel to A F draw 3, 0; parallel to F G draw 0 R; parallel to A F diaw 4 Q; 

parallel to J H draw Q P. Again at Fig. 2 , baluster 1, make V L equal V L of Fig. i; at bal¬ 

uster 2 make S M equal S M of Fig. i; at baluster 3 make 0 R equal 0 R of Fig. i; at 
baluster 4 make Q P equal Q P of Fig. i. Through the points N L M R P H trace the centre 
line of wreath-piece; set off half the thickness of rail each side of the centre as shown by 
the dotted lines. To find the length of 'Any of these balusters proceed as before directed. 

Fig. 3. Face-mould from Plan Fig. i. Quarter-circle B E, also Showing the Squaring 
of the Wreath-piece at Both Joints. —Draw the lines D C and C H at right angles. Make 
C D equal C D of Fig. i; make C B equal C B of Fig. i; make B H equal 3 " for straight 
wood. Make C K M equal C K M of Fig. i; draw K I parallel to C B; draw Q N through M 
parallel to C B; draw the joint D parallel to C B; draw I T parallel to D C; make the joint 
at H at right angles to C H; from T nnd I parallel to C H draw lines to the joint H; make 
C A and K J each equal C H and T U of Fig. i; make M N and M Q each equal S N and 
S W of Fig. i; make D Y and D X each equal E Y of Fig. i. Through T A J Q X of the con¬ 
vex and I N Y of the concave trace the curved edges of the face-mould. The angle with which 
to square the wreath-piece at joint H is contained in the bevel at D of Fig. i. The sides of the 
wreath-piece at joint D are at right angles to the face of plank, and the over-wood is taken 
off both surfaces of the plank equally. Hand-rails ?nuch thicker than two thirds of their width 
require C 07 isiderably greater width and thickness of stuff to work out the wreath-piece. 

Fig. 4 . Plan of Quarter-circle taken from J E of Fig. i, together with Angles of 
Inclination over the Plan Tangents Lettered Alike.— Connect F K; through E and J draw 
E L indefinitely; on F as centre with F H as radius describe the arc H L. Parallel to F K 
draw Y D and V B; parallel to F G draw Z X and N C. 

To Find the Angle with which to Square the Wreath-piece at Both Joints: —Pro¬ 
long F J to P indefinitely; make J P equal J M; connect P K: then the bevel at P will con¬ 
tain the angle required. 

Fig. 5. Face-mould from Plan Fig. 4; also Showing the Squaring of the Wreath- 
piece at Both Joints, and the Additional Width Required by a Form of Hand-rail of this 
Proportion. —Draw the line E H indefinitely; make W H and W E each equal W L of Fig. 4 . At 
right angles to E H draw WG; make W G equal W F of Fig. 4 ; connect G E, G H and G W; make 
G C X, G C X equal the same of Fig. 4 . Through G C X each side of the centre parallel to G W 
draw D Y, B V; make X Y and X D at each end equal Z Y and Z D of Fig. 4 ; make C K V and 

C B each side of the centre equal N K V and N B of Fig. 4 ; make G T S U equal F T S U of 

Fig. 4 ; through H and through E draw Y 0; make E 0 equal E Y; make H 0 equal H Y; 

make H A equal H A of Fig. 2; from 0 and Y draw lines to joint A parallel to G A; through 

ODBTBDO of the convex and through Y V U V Y of the concave trace the curved edges 
of the face-mould. The joints A and E of the wreath-piece are squared by the angle con¬ 
tained in tlie bevel at P of Fig. 4 . By laying out the squaring of the joint as here given, 
the thickness and width of wood required to work out the wreath-piece are found,* and with 
half this width as radius on each of the centres E K S K H A describe arcs of circles, touch¬ 
ing which the edges of a parallel pattern may be traced; or no pattern need be made, and 
the increased width of wood required may be scribed from the edges of the face-mould on 
the plank. The development of a centre line of wreath is given in detail at Plate No. 20, Figs. 

T and 2. Face-mould Fig. 3 is given in detail at Plate No. 10. Face-mould Fig. 5 is given in 
detail at Plate No. ii. 


* Se? Plate 56, Figs, 6 and 7, 













Scale V/z i n = 1 ft. 
































































































PLATE 44. 

Fig. I. A Superior Plan of Starting a Stairs making a Quarter-turn, with Parallel 
Steps and Platform, in about the Same Space Required when Planned with Winders.— 
This plan is given at Plate No. 7, Fig. 8. Describe the plan of rail and its centre line; draw 
the tangents D B and B A, and space the balusters as required; then before proceeding further 
the elevation must be set up. 

Fig. 2. Elevation of Treads and Risers as given at Plan Fig. i and as Figured; 
also the Development of the Centre Line of the Wreath. —Draw the treads and rises as 
shown on the plan, taking the measure—on the centre line of the rail—of each tread in two 
parts as before explained. Place the chord-line A F as at S on the plan Fig. i. Let the 
bottom line of rail rest on X X, the centres of short balusters; draw the centre line of rail 
QE indefinitely and parallel to XX; make FE equal D B of Fig. i; draw EG parallel to the 
chord-line; make 1 S equal four inches, and S B half the thickness of rail; parallel to the floor- 
line draw B D; make D B equal G C: then B is a fixed point, and E is also a fixed point 

at the place where the line G E intersects the centre line of rail T A. Connect E B; and 

where the line C D intersects the line E B at C, draw the line C G at right angles to 
CD. 1 Z equals 1 A of Fig. i; make Z V parallel to 1 B. Place the centre of each baluster 
on the steps in position, and number them as at the plan, drawing lines through each par¬ 
allel to the rise-lines indefinitely. Let A T be three inches for straight wood to be put on 

that end of the wreath-piece. At Fig. i make the angle D C B equal D C B of Fig. 2; 

parallel to E C through 3 draw N G, and from H draw H F parallel to A B. 

Fig. 3. Plan of Rail Quarter-circle D S of Fig. i, with Centres of Balusters 4, 5 
and 6 in Place on the Centre Line. — Make the angle F A E equal F A E of Fig. 2 ; make the 
angle E H J equal G E C of Fig. 2 ; make E P equal F A; draw P Q parallel to E J; draw Q T 
parallel to H E; connect T N, the directing level line; parallel to T N draw X I, E Y, 5, 2 and 
'W V; parallel to E H draw 2 R and 4 U; parallel to F A draw 0 C. At Fig. 2 baluster 1 hap¬ 
pens to be at the point B; at baluster 2 make N K equal I F of Fig. i; at baluster 3 make 
J H equal J G of Fig. i; at baluster 4 make L U equal 4 U of Fig. 3; at baluster 5 make 

P R equal 2 R of Fig. 3; at baluster 6 make 0 Q equal 0 C of Fig. 3; through V K H U R Q A 

trace the centre line of the wreath. Set off each side of the centre half the thickness of rail 
as shown by the dotted lines. To find the length of balusters proceed as before directed. 

Again, at Fig. 3, parallel to F E draw C G; at right angles to T N draw F L and J K; on E 

as centre with E A as radius describe the arc A L; again, on E as centre with H J as radius 
describe an arc at K; connect K L. 

To Find the Angle with which to Square the Wreath-piece at the Joint over J:— 
Prolong F N to M; make N M equal T S; connect M J: then the bevel at M contains the angle 
sought. 

To Find the Angle with which to Square the Wreath-piece over Joint F:—Prolong 
E F to D; make F D equal G B; connect D X; then the bevel at D contains the angle required. 

Fig. 4. Face-mould from Plan Fig. 3, also Showing the Squaring of the Wreath- 
piece at Both Joints. —Draw the line A J indefinitely; make Y A and Y W equal Y L and Y K 
of Fig. 3 ; on J as centre with J H of Fig. 3 as radius describe an arc at H; on A as centre 

with A E of Fig. 3 as radius intersect the arc at H; on Y as centre with Y E of Fig. 3 as radius 

test the intersection of the arcs at H;* connect J H, H A and Y H; make H Q U equal H Q U 
of Fig. 3 ; make H C equal E C of Fig. 3 ; parallel to Y H through C draw X I; through Q 
and U parallel to Y H draw Q 8 and V W; make C X and C I equal 0 X and 0 I of Fig. 3 ; 
make H Z 9 equal E Z 9 of Fig. 3 ; make Q 8 equal T 8 of h'lG. 3 ; make U W and U V equal 
4 W and 4 V of Fig. 3 . Through J draw W B; make J B equal J W; through A draw X D; 
make A D equal A X; make A K equal T A of Fig. 2 ; make the joints K and J at right angles 

to the tangents; from X and D draw lines to joint K parallel to H K; through B V Z I D of 

the convex and W 8, 9 , X of the concave trace the curved edges of the face-mould. The slide¬ 
line is made at right angles to the level line Y H. The angle with which to square the wreath-piece 
at joint K is taken by the bevel D of Fig. 3 , and for joint J the bevel M of Fig. 3 . 

Fig. 5. Face-mould from Plan Fig. i. Quarter A D, which Joins the Level Rail; also 
Showing the Squaring of the Wreath-piece at the Joints. —Draw the lines B C and B Z 
at right angles; make B F G C equal the same at Fig. i; make B A equal B A of Fig. i; 

through A draw H E indefinitely and at right angles to B A; parallel to B A draw F H, and 

through G and C, M N and 0 0; make F L equal I L of Fig. i; make G N and G M equal 

J N and J M of Fig. i. Joint C is made at right angles to B C; make C 0 and C 0 each 

equal D 0 of Fig. i; make A Z three inches for straight wood; make the joint Z at right 
angles to B Z; make AE equal AH; draw lines from H and E to joint Z parallel to B Z. 
Through 0 M L K E of the convex and 0 N H of the convex trace the curved edges of the 
face-mould. The sides of the wreath at joint C are made at right angles to the face of the 
plank, f The angle with which to square the wreath at joint Z is taken by the bevel C of 
Fig. I. Face-mould Fig. 4 is explained in detail at Plate No. 12. Face-mould Fig. 5 is 
explained in detail at Plate No. 10. The development of a centre line of wreath as at Fig. 2 is 
given in detail at Plate No. 20, Figs. 3 and 4. 

* In face-moulds of this kind, if the drawing is carefully made, instead of the length of this level line. Y H bemg 

applied as a test, it may be used 7vith the length of either one of the tangents to establish the angular point H. 

t The sides of wreaths are straight vertically, and can be worked correctly only in that direction with suitable hol¬ 
lows and rounds. After a wreath is shaped, if a straight-edge is tried square across the side of it at any point it 
will be found hollow on the concave side and rounding on the convex side. For this reason in cases like face-mould 

Fig. 5. joint C —in fact, at centre joints of all face-moulds—should properly have some over-wood at O O left on in 

marking out the stuff. 4 















Scale 1 Ve i n. = 1 ft 





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PLATE 45 


Fig. I. Plan of a Circular Flight of Stairs Winding Around a Circular Post. —In 

planning these stairs the first thing to do is to fix tlie place of the starting riser. The next 
consideration is tlie landing and head-room. In tliis case the first, or starting, rise becomes 
the landing and seventeenth rise, making one revolution; the whole height—the rises being 8'' — 
is therefore In finding the head-room at a point between the starting and landing rises, 

from the landing deduct lo" floor-beam, and 2 " for floor and plaster; deduct also the bottom 
rise, 8"—all together 20 ", to be taken from leaving g'.Z" head-room. Then, again, the floor 

at the landing is brought on a line of the fifth rise E B, which makes it necessary to deduct 
from the last sum four rises,— 32", —leaving a balance of head-room at that point of 7 '.o 4 The 
post is sometimes cased as sliown. The tread around the line of travel is 7 ", about the least 
that ought to be permitted, if a hand-rail * is put around the post; but if a rail is hung over 
the outside string, then the line of travel would be further out, and give a tread of 9 ^", which 
would leave the plan as it is, ample. If - the staircase is to stand independent of wall or 
partition, the string should be bent laminated—see Plate No. 8, Fig. 5 —as being stronger than 
by any other method. To give support to the string it may be enclosed to the floor from A to C, 
or from A to B, and then set a supporting post at C, and at D suspend the string with a small 
iron rod from the floor-beam of the story above. If the circular post is made large enough, each 
riser can be set into mortices in the post four or five inches, and secured with lag-screws; the 
steps, too, should be let into the post about 2 ”. 

Figs. 2, 3 and 4.—Fig. 2 is a Plan of Stairs such as is given at Plate No. 7, Fig. 8, 
in which the Cylinder, 5" Thick, is Best Built Solid and Veneered, Both Faces for a 
Close String. —The manner of building the solid cylinder is sliown by the two thicknesses of 
staves between the veneers; the straight portion, built with the cylinder from F to N, is so worked 
for the purpose of including the easement at the lower edge of the concave face Fig. 4. 

Fig. 3. The veneer laid mil for the convex face of the cylinder, the lettering agreeing with that 
face on the plan Fig. 2. The vertical and irregular lines are to show the position and lengths 
of staves required for the convex face. 

Fig. 4. The veneer laid out for the concave face of the cylinder, the lettering agreeing with that 
face on the plan Fig. 2. The vertical and irregular lines indicate the lengths and position of 
the staves for the concave face of the cylinder. This veneer is first laid over the prepared, 
rough-staved cylinder, and on the veneer the concave-faced staves are fitted and glued; then the 
convex staves are fitted and glued over these again; and, finally, the convex veneer Fig. 3 is 
glued over the whole. 

Fig. 5. Plan of Quarter Platform Stairs, Showing another Way of Placing the Risers 
Connecting with the Quarter Cylinder. —A riser may be placed at the chord A; 'then taking 
A B—whicli is the tangent to the centre line of rail—and a portion of the other tangent. B D, 
to equal together one tread, as follows: A B = 6^", B C = 3 ^", making 10 " one tread to the place 
of the next riser C. 

See Plate No. 5 , Fig. 10, and Plate No. 37, Fig. 5 . 


* For treatment of hatid-rail over circular stairs see PLATES 53 a}tci 54. 


* 






P L AT E N o . 4 5 . 





























































































PLATE 46. 

Fig. I. A Superior Plan of Stairs Making a Quarter-turn at the Landing, with 
Parallel Steps and Platform, in about the Same Space required when Planned with 
Winders.— This plan "is given at Plate No. 7, Fig. 4. Describe the centre line of rail, and 
draw the tangents at each quarter cylinder. Space the balusters as required. ^ To find the 
angles of inclination over the plan tangents, and other measurements, the elevation must first 
be set up. 

Fig. 2. Elevation of Treads and Rises as given at Fig. i on the Centre Line of 
the Hand-rail ; also the Development of the Centre Line of Wreath-piece. —Place the 
chord-lines—of which there are three needed—as at the plan. Put the centres of balusters 1, 
2 , 3 as given on each tread, and draw lines indefinitely through these centres parallel to the 
rise-lines. From chord-line A make A B equal A B of Fig. i. Through B draw B C parallel 
to the rise-lines; on the line B C—assuming any point C that will raise the wreath a little 
high rather than fix it low—draw C F, the centre line of ramp, and the inclined line over the 
first plan tangent; where this line C F intersects the chord-line at A draw A B at right angles 
to the chord line; make E Y equal E B of F:g. i: then Y becomes a fixed point. Make H Z 

equal P V of Fig. i; draw Z Q at right angles to HZ; make Z 0 four inches, and A Q half 

the thickness of rail: then Q is a fixed point (unalterable if the level rail is to be kept at 

its usual height). Connect Q Y; divide P D in two equal parts at G; make A F four inches 

for straight wood to be left at the lower end of the wreath-piece. Again at Fig. i make the 
angle V Q P equal E D Y of Fig. 2 ; draw T R and W N parallel to U Q; make the angle E D B 
equal E D Y of Fig. 2 ; make ihe angle B C A equal B C A of Fig. 2 ; make B H equal E D; 
parallel to B A draw H Z; parallel to C B draw Z G; connect G F, the directing level line; 
parallel to G F draw 2 M and 1 K; parallel to E D draw M L; parallel to B C draw K J. 
Again at Fig. 2 , baluster 1, make K J equal K J of Fig. i; at baluster 2 make M L equal M L 

of Fig. i; through the points D LJ A trace the centre line of wreath-piece; set off half the 

thickness of rail each side of the centre, as sliown by the dotted lines. 

To Find the Length of Balusters: —Take for example baluster 2: 2 N equals 3 !^", which 
added to 2 '. 2 ", the usual length of shoft baluster at X (between the top of step and the 
bottom of rail), makes the length of baluster 2 between the same points 2 '.^-^". 

Fig. 3. Face-mould from Plan of Rail at the Landing Quarter-circle Fig. i: also 
Showing the Squaring of the Piece at the Joints. —Draw the lines G Q and Q J at right 
angles; make Q R N P equal Q R N P of Fig. i; make P G equal P G of Fig. 2; make Q U 

equal V U of Fig. i; make U J equal 2" for straight wood; make joint G parallel to J Q; 

make T K and joint J parallel to Q G; parallel to J Q draw I T, N W and X P X; make P X 
and P X each equal P X of Fig. i; make R I and Q Y equal S I and V Y of Fig. i; draw lines 
from X and X to joint G parallel to P G; make U K equal U T; from K and T draw lines 
to joint J parallel to J Q; through K V 1 X of the convex and T W X of the concave trace 

the curved edges of the face-mould. The angle with which to square the wreath at joint J is 

taken by the bevel Q of Fig. i. The sides of wreath-piece at joint G are made at right angles 
to the face of the plank, and the over-wood is removed equally from both faces of the plank. 
The dotted lines show the increased width of stuff required to work out the wreath-piece of 
a hand-rail of so much greater depth than width. 

Fig. 4. Plan of Hand-rail, Quarter-circle A E of Fig. i, with its Angles of Inclination 

E D B and B C A.—Let B H equal E D; make H Z parallel to B A, and Z G parallel to C B; 

connect G F, the directing level line; parallel to G F draw V S, B 5 and R I; at right angles 

to G F draw A P and E W, each indefinitely; on B as centre with B D as radius describe the 

arc D W; again on B as centre with C A as radius describe an arc at P; connect P W. 

To Find the Angle with which to Square the Wreath-piece at the Joint over E;— 

Prolong BE to T; make ET equal E M; connect T 5: then the bevel at T will contain the 
angle required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A:— 
Prolong E F to U; make F U equal G N; connect U A: then the bevel at U will contain the 
angle sought. 

Fig. 5. Face-mould from Plan of Hand-rail Fig. 4; also Showing the Squaring ot 
the Wreath-piece at the Joints. —Draw the line A D indefinitely; make X D and X A equal 
X W and X P of Fig. 4 . On A as centre with A C of Fig. 4 as radius describe an arc at B; 

on X as centre with the level line X B of Fig. 4 as radius intersect the arc at B; connect 

A B, D B and X B; prolong B D to G, and B A to F; make A F equal A F of Fig. 2 ; make D G 
equal D G of Fig. 2 ; make the joints G and F at right angles to the tangents; make D K 
equal D K of Fig. 4 ; make BZ4 equal C Z 4 of Fig. 4 ; through KZ4 parallel to B X draw 

S V, L J and IR indefinitely; make K V, K S equal Q S, Q V of Fig. 4 ; make B 0, X 0 

equal the same at Fig. 4 ; make Z L and Z J, 4, I and 4 R equal G J and G L, Y I and Y R of 

Fig. 4 ; through D draw V C; make D C equal D V; through A draw R H; make A H equal A R; 

from R and H draw lines to joint F parallel to B F; from V and C draw lines to joint G 
parallel to B G; through C S 0 L 1 H of the convex and V 0 J R of the concave trace the curved 
edges of the face-mould. Four additional points on the centre line may be measured as shown, 
and a parallel pattern made by describing arcs of circles of a radius to suit the width given 
by the squaring of the joints; or the extra width may be scribed on the plank from the edges 
of the face-mould. The slide-line is drawn at right angles to the directing level line B X. The 

angle used for squaring the joint G is taken from T of Fig. 4 , and for squaring the joint F the 

angle at the bevel U of Fig. 4 . For detailed explanation of face-mould Fig. 3 see Plate No. 10 
and for face-mould Fig. 5 see Plate No. 12 . ’ ’ 




? 


i 

I 


I 


I 




a 
























































































































PLATE 47 . 

Fig. I. Plan of a Part of a Flight of Winding Stairs of which this Portion makes a 
Half-turn.— This plan is given complete at Plate No. 7 , Fig. 3 . Draw the centre line of rail 
and the tangents. Space the balusters as required; then to find angles, measurements, etc., 
proceed to set up the elevation. 

Fig. 2. Elevation of Treads and Rises as given at Plan Fig. i; also the Develop¬ 
ment of the Centre Line of the Wreath. —Place the chord-lines—of which there are two, A 
and G—as given at the plan, and extend the upper one, J D, at an indefinite length. Put the 
centres of the balusters on each step as at the plan, and draw lines through these parallel 
to the rise-lines indefinitely. With a straight edge held in the direction A J mark a point at 
the lower chord, A, and iit the upper chord, J; with the understanding that if J is placed 
lower on the chord-line, then the upper ramp will be lengthened and the wreath brought 
lower; and if A is raised higher on the chord-line, then the lower ramp, already about right, 

would be increased in length and curve. So at pleasure fix A and J; then draw A D at right 

angles to the chord-line; divide D J in four equal parts; make A B equal the tangent A B of 

Fig. i; draw B C parallel to the rise; make B C equal D E; connect C A, and prolong to N 

indefinitely. At right angles to J F draw G H; let G H equal G H of Fig. i; connect H J, and 
prolong to 0 indefinitely; make J 0 and A N each 3 " for straight wood at those ends cf the 

wreath-pieces. Make the joints of ramps at N and 0 at right angles to N C and H 0. Again 

at Fig. i, as the four heights to be raised at each tangent are alike, make all the angles of 
inclination BCA, EFB, H KE and G H J equal B C A of Fig. 2 . Draw the directing level 
lines M B and M H; parallel to M B draw 1 R and 2 S; parallel to B C draw R L; parallel to 

E F draw ST. Again at Fig. 2 , baluster 1, make R L equal R L of Fig. i; at baluster 2, 

make 2 T equal S T of Fig. i; at baluster 3, P K equals H K of Fig. i. Through A LT K J 
trace the centre line of the wreath. Set off each side of the centre half the thickness of 
rail as shown by the dotted lines. 

To Find the Lengths of Balusters: —Take for example baluster 1 : 1 R measures which 
added to 2 '. 2 " —the usual length of balusters at X X between the top of step and bottom of rail— 
makes the length of baluster 1 between the same points 2 '. 3 ^". 

Fig. 3. Plan of Hand-rail, Quarter-circle A E, Fig. i, with its Tangents and Angles of 
Inclination Lettered Alike.—Connect M B, the directing level line. Parallel to M B draw Q P; 
parallel to E F draw 0 N; through E draw A U indefinitely; on B as centre with B F as radius 
describe the arc F U. 

To Find the Angle with which to Square the Wreath-piece at Both Joints: —Pro¬ 
long BE to T; make ET equal E Y; connect T M; then the bevel at T will contain the angle 
required. 

Fig. 4. Face-mould from Plan Fig. 3, also Showing the Squaring of the Wreath- 
piece at Both Joints. — Draw the line U U indefinitely; make V U, V U equal V U of Fig. 3. Draw 

V B at right angles to U V; make V B equal V B of Fig. 3; connect B U and B U; prolong 

B U to W, making U W equal A N of Fig. 2 . The joints U and W are made at right angles 
to the tangents. Make B N and B N each equal B N of Fig. 3. Through N and N parallel 

to B Z draw P R and P R; make N R and N R each equal 0 Q of Fig. 3; make N P and 

N P each equal 0 P of Fig. 3; make V Z equal V Z of Fig. 3. Through U and U draw R S 
and R S, and make U S equal U R at U and U; draw R Y parallel to B U; from S and R 

draw lines to joint W parallel to B W; through S P B P S of the convex and R Z R of the 

concave trace the curved edges of the face-mould. The angle with which to square the tvreath- 

piece at both joints is taken by the bevel T of Fig. 3. For detailed explanation of this face mould 

see Plate No. ii. The development of the centre line of a wreath-piece of this kind is given in 
detail at Plate No. 20 , quarter-circle A C of Fig. i, and AE of Fig. 2. 


I 






























































PLATE 48. 

Fig. I. Plan of the Bottom Part of a Flight of Winding Stairs, Turning One Quarter, 
Starting with a Newel. — The complete plan of this flight of stairs is given at Plate No. 7 , hiG. 3 . 
Draw the centre line of rail, and space the balusters as required ; then to find the length of plan 
tangent A C, and other measurements, proceed to set up the elevation. 

Fig. 2. Elevation of Treads and Rises as Given at Plan; also the Development of the 
Centre Line of the Wreath-piece. —Place the centre of baluster on each step as at the plan, and 
draw lines through these centres parallel to the rise-lines indefinitely. Let the bottom line of 
rail pass through X X, the centres of short balusters on the regular treads; draw the centre line 
of rail 0 C parallel to X X indefinitely ; make B 0 equal — or more at pleasure—for 
straight wood at the upper end of the wreath-piece ; make M V, 6 " and V N half the thickness of 
rail ; through N at right angles to the chord-line draw A C : then A C will be the length of the plan 
tangent A C at Fig. i. And if from C of Fig. i a line is drawn touching the centre line of rail at 
M, it will be the level tangent. 

Fig. 3. Plan of the Centre Line qf Rail and Tangents A C and C M from Fig. i; also 
the Centres of Balusters D, G, J in Place as at Fig. i.—Through A draw T B at right angles to 
AC; make A B equal A B of Fig. 2 ; connect B C. T is the centre of the circle, and T M is at 
right angles to C M as at Fig. i. Through the centres of balusters J, G, D, and parallel to the 
level tangent M C, draw J K, V H and S E; parallel to A B draw E F, H I and K L; from A diaw 
A P at right angles to the level tangent CM; on C as centre with C B as radius describe the arc 
B P ; connect F* M. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A:—From 
E parallel to C B draw E R indefinitely ; prolong C A to Q ; make A Q equal A R ; connect Q S. 
Then the bevel at Q contains the angle required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over M: —Make 
U V equal H I ; connect V M. Then the bevel at V contains the angle sought. Again at Fig. 2, 
lialuster D, make E F equal E F of Fig. 3 ; at baluster G, make H I equal H I of Fig. 3 ; at baluster 
J, make K L equal K L of Fig. 3 . Through the points B F I L N trace the centre line of the 
wreath-piece; set off each side of the centre half the thickness of rail as shown by the dotted lines. 

To Find the Lengths of Balusters :—Take for example baluster D; D S measuring 4 ^", whicli 
must be added to 2 '. 2 "—the length of short baluster at X from the top of step to the bottom of 
the rail—making the length of the baluster D between the same points 2 . The height of rail 

at the newel is calculated by adding M V, 6 " to the length of short baluster at X, 2 '. 2 '; making the 
height from M to V 2 '. 8 ". 

Fig. 4. Parallel Pattern for Wreath-piece from Plan Fig. 3; also Showing the Squaring 
of the Wreath-piece at the Joints. — Make M B equal M P of Fig. 3 . On B as centre wiih B C 
of Fig. 3 as radius describe an arc at C; on M as centre with M C of Fig. 3 as radius intersect 
the arc at C; connect C M and C B; prolong C B to 0; make B 0 equal B 0 of Fig. 2 . Make 
M W equal M W of Fig. i. Make the joints 0 and W at right angles to the tangents. Make 
B F 1 L equal to B F I L of Fig. 3 . Make F D, I G and L J equal E D, H G and K J of Fig. 3 . 
On the centres B D G J M with a radius equal to half the required width of the pattern 
describe circles, and touching these trace the edges of the pattern. The angle with which to 
square the wreath-piece at joint 0 is taken by the bevel Q of Fig. 3 , and the angle for squaring 
the w'reath piece at joint W is taken by the bevel at V of Fig. 3 . The development of a centre 
line geometrically the same as this of Fig. 2 is given at Plate No. 2t, Figs, i and 2. Face-mould 
and parallel pattern as required by this plan are treated geometrically in detail at Plate No. 14. 


% 






Scale 1H In = 1 Ft. 
























































PLATE 49. 

Fig. I. Plan of the Bottom Portion of a Flight of Winding Stairs, this Part of the 
Flight Turning a little more than a Quarter and Starting from a Newel.— This case of 
hand-railing is geometrically the same as that given at Plate No. 48 . In the last-mentioned 
Plate the cylinder is 10 " in diameter, embracing three winders; but the plan here presented 
has a cylinder 20 " in diameter, containing five winders. The object of introducing this example 
is to demonstrate the correctness and practicability of working the wreath around a large 
cylinder in one piece, showing, too, by tlie development of the centre line of the wreath its 
exact position and relation to step and rise. The length of plan tangent A B cannot be deter¬ 
mined until the elevation is drawn, if a fixed height of rail at the newel is required. 

Fig. 2. Elevation of Treads and Rises as at Plan; also the Development of the 

Centre Line of Wreath-piece. —Let the bottom line of rail pass through X X, the centres of 
sliort balusters on the regular treads; draw the centre line of rail F B parallel to X X indefi¬ 
nitely; make 1 E equal 8 '', and E G half the thickness of rail. Through G draw B A at right 

angles to the chord-line. Again, at Ffo. i, continue the centre line of rail to B, and make 

A B equal A B of Fig. 2; make A C at right angles to A B and equal to A C of Fig. 2; from 
B draw B Z tangent to the centre line of rail; from H, the centre of the cylinder, draw 
H 0 at riglit angles to B Z; then B 0 is the level tangent. Place the balusters as required, 
and number those that come under tlie wreath. Tlirough balusters 2, 3, 4 and 5 draw S 8 , 
F 7, I. 6 , 5 T, and from P, P R, all parallel to OB; parallel to AC draw T K, Q L, 6 N, 7 J 
and 8 , 9. 

To Find the Angle with which to Square the Wreath-piece at the Joint over Z:— 

Make G F equal 7J; connect F 0: tlien the bevel at F contains the angle required. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A: — 
From N draw N M parallel to A B; make A E equal M K; connect E I: then ihe bevel at E 
contains the angle sought. From A draw A D indefinitely and at right angles to BO; on B 
as centre with B C as radius describe the arc C D; connect D 0. Again, at Fig. 2 , place the 
centres of balusters on each step as at the plan, and draw lines through these centres parallel 
to the rise-lines. At baluster 2 , make 8, 9 equal 8, 9 of Fig. i; at baluster 3 , make 7 J equal 
7 J of Fig. i; at baluster 4, make 6 N equal 6 N of Fig. i; at baluster 5, make T K equal T K 
of Fig. i; through C K N J 9 G trace the centre line of the wreath-piece; from this centre set 
off each side half the thickness of rail as shown by the dotted lines. Proceed to find the 
lengths of balusters and the height of rail at newel as directed at Plate No. 48. 

Fig. 3. Face-mould from Plan Fig. i; also Showing the Squaring of the Wreath- 
piece at the Joints. —Draw the line CO equal to D 0 of Fig. i; on 0 as centre with 0 B 
of Fig. I as radius describe an arc at B; on C as centre with C B of Fig. i as radius intersect 
the arc at B; connect 0 B and B C: prolong B 0 to Z; make 0 Z equal 0 Z of Fig. i; prolong 

B C to F; make C F equal C F of Fig. 2 ; make the joints Z and F at right angles to the tan¬ 

gents; make C L N J 9 equal the same at Fig. i; and through each of these divisions draw lines 
parallel to BO; make 0 X equal OX of Fig. i; make J W Y equal 7 W Y of Fig. i; make NYU 
equal 6 V U of Fig. i; make L P. L R equal Q P, Q R of Fig. i. Through C draw P E; make C E 
equal C P; make 0 K equal 0 S; draw lines from P and E to the joint F parallel to C B; draw 

lines from K and S to joint Z parallel to B 0; through E R V W X K of the convex and P U Y S 

of the concave trace the curved edges of the face-mould. Joint Z of the wreath-piece is squared 
by the angle contained in bevel F of Fig. 1, and joint F is squared by the angle contained in 
bevel E of Fig. i. 

Fig. 4. A Sketch of this Wreath-piece as it Appears when Squared up. 






Plate N“ 49 


w 



































































































PLATE 50. 

Hand-rail over Steamboat Stairs, from Plan given at Plate No. 6, Fig. 9. — Fig3. i, 2 and 3 are 
together the plan of the string with its different curves, including the whole number of treads. Describe the 
centre line of rail and on this centre line place the balusters on each step numbered as shown. The 

intention is to take two treads in the first piece of rail from A to C, and in the second piece of rail to 

include six treads from C to N; the third piece of rail to take the two last treads with as much more as 

it requires to bring this top wreath-piece to a level at the required height. Draw ihe level tangent A B 

at right angles to A J; through C draw B K at right angles to J D; through N at right angles to N, 4, 3 
draw K 0 indefinitely; the point 0 must now be established by measuremient taken from the elevation. 

Fig. 4. Elevation of Treads and Rises as given at Plan; also the Development of the 

Centre Line of Wreath, including the Whole Flight.— On the line of the third rise C D fix D 
distant from baluster 3, so that the bottom line of rail will pass through 3; draw D K at right angles to 
D C; make D K equal C K of Fig. 2 ; draw K L parallel to the rise-lines, and equal to three rises; connect 

L D, and prolong to B indefinitely; make C B equal C B of Fig. i where the length of tangent C B 

intersects the inclined line D B at B; draw C A through B at right angles to CD; touching L draw 

G N at right angles to L K; prolong the ninth rise to M and N; make N G equal N K of Fig. 2; make 

N M equal three rises; connect M G; draw M 0 at right angles to M N; make 40,41 equal four inches; 

make 41, P equal half the thickness of rail. Again at Figs, i, 2 and 3, make N M of Fig. 2 at right 
angles to K N, and equal to three rises; then at Fig. 3 make 0 P equal 0 P of Fig. 4; draw P, 39 

parallel to 0 N; from N parallel to K M draw N P; from P draw PO parallel to M N; from 0 draw 

the line 0 T, touching the centre line of rail; from the centre V draw V S at right angles to 0 T: then 
0 S will be the level tangent; parallel to 0 S draw 12, 36; 11 , 34 and Z 10, 33; parallel to 0 P draw 

36, 37; 34, 35; 33, R and 9, 38. 

To Find the Angle with which to Square the Wreath-piece from Fig. 3 over Joint N;— 

Make N, 42 equal 33, 32; connect 42, Z: then the bevel at 42 contains the angle required. 

To Find the Angle with which to Square the Wreath-piece from Fig. 3 at the Joint over 
S:—From R draw R 13 parallel to N 0; make ST equal 13, P; connect T U: then the bevel at T 
contains the angle sought. From N at right angles to S 0 draw N X indefinitely; on 0 as centre with 
N P as radius describe an arc at X; connect X S. At Fig. 2 make K L at right angles to C K and equal 
to three rises; connect L C; parallel to C L draw B D of Fig. i; from C through N draw C Q indefinitely; 
on K as centre with K M as radius describe the arc M Q; connect K, 43; parallel to K W draw 8 , 27; 
7. 25; 6 , 23; 5, 21 and 4, 19; parallel to N M draw 27, 28; 25, 26 and 23, 24; parallel to K L draw 21, 22; 
19, 20 and 3, 18. 

To Find the Angle with which to Square the Wreath-piece from Plan Fig. 2 at Both 

Joints: —Draw 28, 29 parallel to K N; make N, 31 equal 29, 30; connect 31, Y: then the bevel at 31 

contains the angle required. At Fig. i, parallel to A B, draw 1, 16 and 2, 14; parallel to C D draw 14,15 

and 16,17; from C draw C E at right angles to A B; on B as centre with B D as radius describe the 

arc D E; connect E A. 

To Find the Angle with which to Square the Wreath-piece from Plan Fig. i at the Joint 
over C:—Prolong line of joint C D, and level line A B, to G; make C F equal C, 15; connect F G: then 
the bevel at F contains the angle required. 

To Find the Angle with which to Square the Wreath-piece from Plan Fig. i at the Joint 
over A:—Parallel to BA draw C I; make H I equal C D; connect I A: then the bevel at I contains the 

angle sought. Again at Fig. 4: take all the heights from the plan tangents of Figs, i, 2 and 3, and 

place them on the lines drawn through the centres of like-numbered balusters, and as shown by the 
other corresponding numbers and letters; and through these top-numbers and letters trace the centre 
line of wreath. The governing length of baluster on this flight ought to be 2 '. 4 " at its centre, from 

top of step to bottom of rail. The odd lengths of balusters will be found as before explained. In case 

the bottom line of rail falls below the step or floor-line, at the cent.'-e line of baluster—as, for instance, 
here at baluster 11 —then that distance must be subtracted from the length of the governing baluster; 
the remainder will be the length of baluster 11 . 

Fig. 5. Parallel Pattern from Fig. 3 for Wreath-piece, Joining Level Rail at Top; also 

Showing the Squaring of the Wreath-piece at the Joints. —Make S N equal S X of Fig. 3 ; on N as 

centre with N P of Fig. 3 as radius describe an arc at P; on S as centre with SO of Fig. 3 as radius 

intersect the arc at P; connect S P and P N; make N 38, R 35, 37 equal the same at Fig. 3 ; make 

37. 12 equal 36, 12 of Fig. 3 ; make 35, 11 equal 34, 11 of Fig. 3 ; make R 10 equal 33, 10 of Fig. 3 ; 
make the joints N and S at right angles to the tangents. Through N, 38, 10, 11, 12 and S as centres, 
with a radius equal to half the width of the required pattern, describe circles, and touching these trace 
the edges of the pattern. To square the wreath-piece at joint N take the bevel 42, and for squaring 
the wreath-piece at joint S take the bevel T. 

Fig, 6. Parallel Pattern for Wreath-piece over Six Treads; also Showing the Squaring of 
the Wreath-piece at the Joints. —Make W M and W C each equal W Q of Fig. 2 ; draw W L at right 

angles to W M; make W L equal W K of Fig. 2 ; connect L M and L C; make the joints C and M at 

right angles to the tangents; make C 18, 20, 22 equal the same at Fig. 2 ; make L, 24. 26 and 28 equal 
K, 24, 26 and 28 of Fig. 2 ; parallel to L W draw 28, 8 ; 26, 7; 24, 6 ; 22, 5; 20, 4; make 20,4 equal 19, 4 of 

Fig. 2 ; make 22,5 equal 21, 5 of Fig. 2 ; make 24,6 equal 23,6 of Fig. 2 ; make 26,7 equal 25,7 of 

Fig. 2 ; make 28, 8 equal 27, 8 of Fig. 2 . Through C, 18, 4, 5, 6 , 7, 8 , M as centres with a radius equal to 
one half the width of the required pattern describe circles, and, touching these, trace the curved edges of 
the pattern. Both joints of this wreath-piece are squared by the bevel at 31 of Fig. 2. 

7 - Parallel Pattern for Wreath-piece Joining the Newel at the Starting, and In¬ 
cluding the Two First Treads; also Showing the Squaring at the Joints of the Wreath-piece.— 
Make A D equal A E of Fig. i. On D as centre with D B of Fig. i as radius describe an arc at B; on A 
as centre with A B of Fig. i as radius intersect the arc at B; connect B D and BA; make the joints 
A and D at right angles to the tangents; make B, 17, 15 equal the same at Fig. i; make 17,1 and 

15,2 equal 16,1 and 14,2 of Fig. i; through A, 1, 2, D as centres with a radius equal to one half 

the required width of pattern describe circles, and, touching these, trace the edges of the pattern. The 
angle with which to square the wreath-piece at joint D is taken by the bevel F at Fig. i, and for joint 
A the angle is taken by the bevel I of Fig. i. Face-vwiilds and parallel patterns are treated in detail at the 
following Plates: Fig. 5 at Plate No. 14; Fig. 6 at Plate No. 15; Fig. 7 at Plate No. 13. Development of 
the centre lines of wreaths is given in detail at the folloiving Plates and Figures: Fig. 5 at Plate No. 21, Figs, i 

and 2, and of Fig. 6 at the same Plate, Figs. 7 and 8; Fig. 7 at Plate No. 20, Figs, s and 6. 



Plate N? 50 



























































Fig'. I. Plan of Stairs Showing how to Place Parallel Steps of a Uniform Width in 
a Large Cylinder, Avoid Winders, and Make Use of the Room Afforded by Securing a Full 
Platform; also an Evenly-graded Hand-rail in Three Parts, Free from Abrupt Top 
Curves or Ramps. —This plan is given at Plate No. 6, Fig. 8. Describe the centre line of rail; 
set off and number the balusters coming within the cylinder as shown. Divide the cylinder into 
three equal parts by the radials R, 29, and R I; draw tangents to the centre line of rail as fol¬ 
lows: At right angles to R U draw U 16; througli A at right angles to R, 29 draw 16 B; through 
10 at right angles to R I draw B 35; at light angles to R 42 draw 43, 35; at right angles to A B 
draw B D indefinitely; at right angles to B 35 draw 35, 34 indefinitely; at right angles to U 16 
draw 16, 15 indefiniielv. Further measurements required will be obtained from the elevation. 

Fig. 2. Elevation of Treads and Rises as given at Plan Fig% i; also the Develop¬ 
ment of the Centre Line of Wreath. —Place the centre of baluster on each step and number 
them as at the plan. Through each of the centres draw lines parallel to the rise-lines indefinitely. 
Let the bottom line of rail at the upper and lower ends pass through X X and I X, the centres of 
short balusters; parallel to X X draw the centre line of rail B 34, parallel to 1, X draw the centre 
line of rail A 15; at right angles to the chord-line draw U 45; make U 45 equal the tangent 
U 16 of Fig. i; parallel to the chord-line draw 45, 15; parallel to U 45 draw 15 F indefinitely; 
make 43, 34 equal 43, 35; parallel to the chord-line draw 34 F; draw 34, 43 at right angles to 
the chord-line; divide F 34 into four equal parts and draw lines through each division par¬ 
allel to F 15 indefinitely. Make 42 B and U A each three inches for straight wood to be added 
to the upper end of one and the lower end of the other wieath-piece, connecting with the 
straight rail. Again, at Fig. i, make 16, 15 equal 16. 15 of Fig. 2 ; connect 1 5, U; make 
43.42 equal the same at Fig. 2; connect 42,35. Set up the following heights; 35,34; 10, I; 
B D and A 29—each equal one of the four equal heights at 34 F of Fig. 2 . Connect 34. 10; 

I B, D A and 29, 16; make 42, 44 equal 35. 34; draw 44. 38 parallel to 43, 35; make 38, 36 
paiallel to 43,42; diaw 43,37 parallel and equal to 35, 10; connect 36,37; parallel to 36,37 
draw 1 1,30, 12,32 and 13.39; parallel to 43,42 draw 14,41, 39.40 and 36,38; parallel to 
35, 34 draw 32, 33 and 30, 31. Make 16, 17 equal A 29; draw 17, 19 parallel to 16 U; draw 
19, 23 parallel to 16, 15; make U 25 parallel and equal to 16 A; connect 25, 23; parallel to 
25. 23 draw 4, 26. 3, 24 and 2, 20. Parallel to A 29 draw 5, 28 and 26, 27; parallel to 16, 15 

draw 24, 18; 20, 21 and 1. 22. At the middle piece of hand-rail describe half its width each 

side of the centre line. Through A and 10 draw A 0 indefinitely; at right angles to A 10 draw 
B P; p irallel to B P draw E F, Y T, 8 C and 7 N; parallel to B D draw N M and 6 L; parallel 
to 10. 1 draw X H, Z G and C K; on B as centre with B I as radius describe the arc I, 0. 

To Find the Angle with which to Square the Wreath-piece at Both Joints: —Prolong 
T Y to W; draw G J parallel to 10 B; make 10 S equal J H; connect S W: then the bevel at 
S contains the angle required. Again, at Fig. 2 , take all the heights from the plan tangents at 
Fig. I and place tliem on the lines drawn through the centres of like-numbered balusters, and as 
shown by the other corresponding numbers and letters; and through the top numbers and letters 
trace the centre line of wreath. The odd lengths of balusters will be found as before explained. 

Fig. 3. Face-mould for the Middle Piece of Hand-rail; also Showing the Squaring 
of the Wreath-piece at the Joints. —Make V 0 and V A each equal V 0 of Fig. i; make 
P D equal P B of Fig. i; connect A D and 0 D; make D G H and D G H equal B G H of Fig. i. 

Parallel to P D through G, H and G, H draw E F and Y T; make D Q V equal B Q V of Fig. 1 ; 

make G T, G Y, G T, G Y equal Z T, Z Y of Fig. i; make H F, H E, H F, H E equal X F, X E of 
Fig. i; through A draw E S; make A S equal A E; through 0 draw E B; make 0 B equal 0 E. 
Make the joints A and 0 at right angles to the tangents. Through SFTQTFB of the 

co.nvex and E Y P Y E of the concave trace the curved edges of the face-mould. The angle for 

squaring the wreath-piece at joints 0 and A is taken by the bevel S of Fig. i. 

Fig. 4. Plan of the First Third of the Wreath, with the Tangents and Angles of 

Inclination from U to A of Fig. I.—Make U K parallel and equal to 16 A; make 16, 0 equal 
A 29; make 0 N parallel to U 16; make N M parallel to 15, 16; connect M K, the directing 
level line; parallel to M K draw Q S, W L, 16 D, Z F and J I; parallel to Q 29 draw V T and 
X Y; parallel to 16, 15 draw 2, 4 and 6 , 3; at right angles to K M draw A B and U H; on 16 

as centre with 16, 29 as radius describe the arc 29 B; again, on 16 as centre with U 15 as 

radius describe an arc at H; connect H B. 

To Find the Angle with which to Square the Wreath at the Joint over A:—Make 
A E equal AT; connect E D: then the bevel at E contains the angle required. 

To Find the Angle with which to Square the Wreath at the Joint over U :—Draw 

F G at right angles to F U; make F G equal 2, 5; connect G U: then the bevel at G contains 
the angle sought. 

Fig. 5. Face-mould over the Plan Fig. 4, also Showing the Squaring of the Wreath- 
piece at the Joints. —Make B C H equal B C H of Fig. 4 ; on H as centre with U 15 of Fig. 4 
as radius describe an arc at 16; on C as centre with C 16 of Fig. 4 as radius intersect 

the arc at 16; connect B 16, C 16 and 16 H; make 16, 2, 3 equal 15, 4, 3 of Fig. 4 ; make 16, 

Y, T equal 16, Y, T of Fig. 4 ; parallel to C 16, through T, Y, 2, 3, draw J I, 8 Z, W L and Q S; 

make 3, I, 3 J, 2 Z, 2 8 equal 6 I, 6 J, 2 Z and 2, 8 of Fig. 4 ; make 16, P, G equal 16, P 9 of 

Fig. 4 ; make Y L, Y W, T S and T Q equal X L, X W, V Q, V S of Fig. 4 . Through H draw J E; 

make H E equal H J; through B draw Q F; make B F equal B Q; make H D equal U A or 

42, B of Fig. 2 . Make the joints D and B at right angles to the tangents. Draw lines from 
E and J to joint D parallel to 16, H; through E I Z P L S F of the convex and J 8 C W Q of 

the concave trace the curved edges of the face-mould. Make the slide-line at right angles to 

the level line C 16. Joint B of the wreath-piece is squared by the bevel at E of Fig. 4 , and 
joint D is squared by the bevel at G of Fig. 4 . A face-mould geometrically the same as 
Fig. 3 is given In detail at Plate No. 15 , and a face-mould geometrically the same as Fig. 5 
is also given in detail at Plate No. 16 . Development of the centre line geometrically the 
same as the centre line of this wreath-piece from U to A of Fig. i is given in detail at 
Plate No. 21 , Figs. 9 and 10 ; also an example of the development of a centre line of wreath 
from A to 10 of Fig. i is given geometrically the same in the last-mentioned Plate, Figs. 7 
and 8 . 


P L AT E N O. 5 1 . 


Platform 


D 








































































PLATE 52. 

Fig. I. Plan of a Platform and Double-landing Steamship Staircase with Newels at 
the Starting, at the Angles of the Platform and at the Landings. —The posts at the starting 
are intended to run above the upper deck a sufficient height to receive the level hand-rail and 
balustrade of that deck as shown by the dotted lines. All the newel-posts are to be finished 
above the hand-rails with moulded caps, the landing-post also finished with moulded drops 
below the strings. The platform-posts are to rest on the lower deck. A plan of a staircase 
similar to this with a continued hand-rail is given at Plate No. 6, Fig. 9, the hand-rail of 
which is treated at Plate No. 50 . 

Fig. 2. Elevation of Treads and Rises between the Starting Newel and the Plat¬ 
form Newel. —The treads in the curve from A to F on the plan must be measured on 
the centre line of rail in the manner before directed,—taking each tread in two parts. Place 
the centres of the three balusters in the curve as numbered in position on each tread, and 
through these draw lines parallel to the rise-lines indefinitely. Make A E equal A D of Fig. i 
through E draw E D parallel to the rise-lines; make D F equal D F of Fig. i; continue the 
tread-line M to F and Z; from X, the centre of baluster, with a radius equal to half the 

thickness of rail describe an arc at U; touching U draw a line to F; at E draw the line EA 

at right angles to E D; through X parallel* to U F draw the bottom line of rail X C; make B N 
equal 3 " for straight wood to be left on the upper end of the wreath-piece. At right angles to 
F E draw F W; make F W equal half the thickness of rail; draw W Y parallel to E F. 

Fig. 3. Plan of Rail with Centre Line and Tangents taken from A to F of Fig. i.— 
Make A B at right angles to A D and equal .A B of Fig. 2 . Connect B D; at right angles to 
D F draw D E equal to D E of Fig. 2 ; connect E F; connect D K; through A draw F C indefi¬ 
nitely; on D as centre with D B as radius describe the arc B C. The numbers 1, 2 and 3 desig¬ 
nate the centres of the first th'ree balusters as placed on the treads at Fig. i. Parallel to 

G D draw P Q, 3, 0 and 2 Z; parallel to D E draw Z T and 1 R. 

To Find the Angle with which to Square the Wreath-piece at Both Joints Pro¬ 
long D F to J indefinitely; make FJ equal D H; connect J K; then the bevel at J contains 

the angle sought. Again, at Fig. 2 , take the heights 0 V, Z T and 1 R from Fig. 3 and place 
them at the like-numbered balusters as shown ; then through M R T V B trace the centre-line 
of wreath-piece; below this centre line set off half the thickness of rail for the bottom line 
of wreath. Find the odd lengths of balusters as before explained, first fixing the length of 

baluster at X to suit, which should not be less than 2 '.from top of step to the bottom of 

rail at the centre of baluster. 

Fig. 4. Face-mould from Plan Fig. 3; also Showing the Squaring of the Wreath at 
the Joints. —Make G C, G C each equal G C of Fig. 3. Draw G D at right angles to G C; 
make G D equal G D of Fig. 3; connect D C, D C, and prolong each indefinitely; make C Y 
equal W Y of Fig. 2; make C N equal B N of Fig. 2; make the joints N and Y at right angles 

to the tangents; make D U, D U each equal D U of Fig. 3. Parallel to G D draw U P, U P; 

make U P, U P each equal Q P of Fig. 3; make D X X equal D X X of Fig. 3; through C and 

C draw P L and P L; make C L and C L equal C P; draw lines from P and L to the joints 

parallel to the tangents; through L X L of the convex and P X P of the concave trace the 

curved edges of the face-mould. The dotted lines show the extra width of wood required— 
greater than the width of face-mould—to get out the wreath-piece with this proportioned form 
of hand-rail. This wreath-piece is squared at the joints Y and N by the angle at bevel J of 
Fig. 3. An elementary study of a face-mould geometrically the same as this is given at Plate 
No. 15; also a like study of the development of a centre line of wreath geometrically the 
same as at Fig. 2 is given at Plate No. 21, Figs. 7 and 8. 




face: op newel at platform 


r 





























































































06 . 

Hand-rail for Circular Staircase from Plan given at Plate No. 7, Fig. lO.—F igs, i, 2 

and 3 are together the plan of the string with its curves, includi^ the whole number of 
treads. Describe the centre line of rail greater radius than the front-string. The hand-rail 
of this flight is divided into five parts: Fig. i from the newel-post A to D embraces three 
treads, and three more divisions of the hand-rail will each include five treads; the fifth piece 
of rail will take the last tread, and as much more of the curve as it requires to bring this 
top wreath-piece to a level at its proper height. Draw the tangents to the centre line of 
rail as follows' At right angles to the radial Y E, touching D, draw B 1; at right angles to 

the radial Y C, touching C, draw 1 F; at right angles to the radial Y L, touching L, draw 4 F; 

at right angles to Y X, touching X, draw U 4; at right angles to D 1 draw 1, 2; make 1, 2 

equal two rises and a half, the rise being 7 ^"; connect 2 D; make C 3 and F E each at right 

angles to 1 F, and each equal to two and a half rises; connect 3, 1, also E C; at right angles 
to F 4 draw 4,5; make 4,5 and LJ each equal two and a half rises; connect 5 L, also JF; 
make X 6 equal two and a half rises; connect 6 , 4. At Fig. 2 , through L draw C K indefinite!}'; 

on F as centre with F J as radius describe the arc J K; from M parallel to Y F draw M N, 

Q R and H F; parallel to L J draw 0 T and PS. 

To Find the Angle with which to Square the Wreath-piece at Both Joints:— 

Parallel to F Y draw A G; at right angles to Y C draw A B; make A B equal G D; connect BC: 

then the bevel at B contains the angle sought. At Fig. i the curve of string which includes 

the two first treads has a radius I Z equal to one foot; also, the limit of tangents D B and B A 
cannot be determined until a portion of the elevation is set up; neither can the tangents X U 
and U B of Fig. 3 be fixed, for the same reason. 

Fig. 4. A Portion of an Elevation of Treads and Rises, including the Three First 

Treads, the Top Tread, and Landing. —Let the bottom line of rail pass through XXX, the 
centres of balusters; make W T equal 8 ", and T Z half the thickness of rail; draw Z D parallel 
to line of tread; prolong the fourth line of rise to C and D; draw C U at right angles to C D 
indefinitely; make S E equal 4 ", and E V half the thickness of rail. Again at Fig. i, make D C 

equal D C of Fig. 4 ; parallel to 2 D draw C B; from B draw the tangent B A, touching the 

centre line of rail; from 1 at right angles to B A draw I A; from D at right angles to B A 

draw D H indefinitely; on B as centre with B C as radius describe the arc C H; connect H A; 

parallel to B A draw P Q, R X and V W; parallel to D E draw 0 F, S M and U N. 

To Find the Angle with which to Square the Wreath-piece at the Joint over D:— 

Parallel to A B prolong R X to E; from .S draw S L parallel to B C; make D G equal D L; 

connect G E: then the bevel at G contains the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over A:— 

Let D J be parallel to B A; make K J equal D C; connect J A: then the bevel at J will contain 

the angle required. At Fig. 3 , make U V equal U V of Fig. 4 ; draw V W parallel to U X; from 

X parallel to 6 , 4 draw X V; from V at right angles to X U draw V U; from U draw U C, 
touching the centre line; from Y at right angles to U C draw Y B; from X at right angles 

to U B draw X H indefinitely; with X V as radius on U as centre describe an arc at H; 

parallel to B U draw A G, E K and X D. 

To Find the Angle with which to Square the Wreath-piece at the Joint over X:— 

Make X F equal Z 0; connect F G: then the bevel at F contains the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over B:— 

Make B C equal U V; connect C D: then the bevel at C contains the angle required. 

Fig. 5. Face-mould from Plan Fig. i; also Showing the Squaring of the Wreath- 
piece at the Joints. —Make C A equal A H of Fig. i. On C as centre with C B of Fig. i as 

radius describe an arc at B; on A as centre with A B of Fig. i as radius intersect the arc 

at B; connect C B and B A; make C F M N equal the same at Fig. i; parallel to A B through 
F M and N draw V W, R S and Q P; make F Q and F P equal 0 Q and 0 P of Fig. i; make 

M R and M S equal S R and S X of Fig. i; make N W equal U W of Fig. i; through C draw 

P T; make C T equal C P; make the joints A and C at right angles to the tangents; make 

A E equal A V; through P S W B E of the convex and T Q R V of the concave trace the curved 

edges of the face-mould. This wreath-piece is squared at the joint C by the angle at bevel 
G of Fig. i, and at joint A is squared by the angle at bevel J of Fig. i. 

Fig. 6. Face-mould from Plan Fig. 2; also Showing the Squaring of the Wreath- 
piece at the Joints. —Make H K, H K each equal H K of Fig. 2 ; make H F at right angles to H K, 
and equal to H F of Fig. 2 ; connect F K and F K; make F S T and F S T equal the same at 

Fig. 2 ; parallel to H F through S T and S T draw M N, Q R and M N, Q R; through K and K 

draw M Z and M Z; make K Z, K Z each equal M K; make F 0 0 equal F X X of Fig. 2 ; make 

S R, S Q, T N, T M each side of the centre 0 0 equal P R, P Q, 0 N and 0 M of Fig. 2 ; make 

the joints K, K at right angles to the tangents; through ZNRORNZ of the convex and 
M Q 0 Q M of the concave trace the curved edges of the face-mould. This wreath-piece is 
squared at both joints by the angle at bevel B of Fig. 2 . 

Fig. 7. Face-mould from Plan Fig. 3 ; also Showing the Squaring of the Wreath- 
piece at Both Joints. —Let B X equal B H of Fig. 3 . On B as centre with B U of Fig. 3 as 

radius describe an arc at U; on X as centre with X V of Fig. 3 as radius intersect the arc 

at U; connect X U and U B; make the joints B and X at right angles to the tangents; make 

X 0 L equal X 0 L of Fig. 3 ; parallel to B U and through X, 0, L draw X J, T G and A M; 

make U N and L M equal U P and Z S of Fig. 3 ; make X J, 0 T, 0 G equal X J, N K, N E of 

Fig. 3 ; make B C equal B A; through X draw G F; make X F equal X G; through G M N C of 

the convex and A T J F of the concave trace the curved edges of the face-mould. The angle 
with which to square the wreath-piece at joint X is taken by the bevel F at Fig. 3 , and for 
joint B the angle is taken by the bevel at C. An elementary study of a face-mould geometrically 
the same as Figs. 5 and 7 is given at Plate No. 13 , and of face-mould Fig. 6 at Plate No. 
15 . A like study of the development of a centre line of wreath-piece geometrically the same 
as required for Figs. 5 and 7 is given at Plate No. 20 , Figs. 5 and 6; also the development 
of a centre line of wreath-piece geometrically the same as required for Fig. 6 is given at 
Plate No. 21 , Figs. 7 and 8 . 


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Scale: in.= 1 


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7 







PLATE 54. 

Fig”. I. Plan of Starting the Circular Staircase given at Plate No. 53, with a Scroll 
Step and Hand-rail instead of a Newel. —The first three steps in this plan are all included in 
the curve of the scroll, but the bottom step is properly the scroll step. The radius Y D is the 
same as that of the plan of circular string, Plate No. 53. D 2, 1 is equal to D 2, 1 at the plan, 
Plate No. 53. Touching D, the tangents 1 A are at right angles to YD; at right angles to D A, 
touching the centre line of rail at F, draw A F; make the joint F at right angles to FA; from 

A parallel to D 2 draw A E; parallel to V E draw U H, I C and G B. 

To Ascertain the Height of the Scrolled Hand-rail, as Regulated by the Tangent DA 
and the Angle of Inclination D E A:—Set up an elevation of the first three treads, including the 

fourth rise as at Fig. 2, Let X be the centre of baluster, and let the bottom line of rail pass 

through X; also let D E A equal D E A of Fig. i. Make A B half the thickness of rail; then 
B C, which is 4 ^", added to whatever height of baluster is given at X, will be the total height 
of scrolls between the top of the first step C and the bottom of the scroll B when the rail 

is set up. The scroll looks best when kept at a height between C and B not exceeding 2 '. 6 '. 

In shaping the top and bottom of the scroll it is desirable not to finish to a level at the joint 

F, but to continue the easing an inch or two lower down, coming to a level with its ease¬ 

ment at about the eye of the scroll. The scroll may also be brought lower by increasing the 
length of tangent D A of Fig. i, forming an acute angle with the plan tangents; or it may 

be fixed at a greater height by lessening the length of tangent D A, and forming an obtuse 

angle with the plan tangents. 

Fig. 3. Face-mould from Plan of Scroll Fig. i; also Showing the Squaring of the 
Wreath-piece at the Joints. —Let E A equal E A of Fig. r; make A F at right angles to A E 
and equal to A F of Fig. i; make E H C B equal the same at Fig. i; through E H C B parallel to 

F A draw V V, U M, I L and G B; make E V, E V, H U, H M, C I, C L, B K and A J equal D V, T U, 

T M, 0 I, 0 L, S K and A J of Fig, i. Through F draw G P parallel to A E; make F P equal 

F G; through P J K L M V of the convex and V U I G of the concave trace the curved edges 

of the face-mould. This wreatli-piece is squared at the joint F by the angle at bevel E of 
Fig, I. At joint E tlie sides of the wreath are at right angles to the plane of the plank. 

Fig. 4. To Draw a Scroll suitable for this Hand-rail and Staircase. —Describe a circle 
of a diameter about sufficient to enclose the spiral line to be developed—its exact diameter 
is unimportant. Divide the circumference of the circle into sixteen parts; make the diameter 
of the eye of the scroll S J equal the width of the hand-rail. The spiral curve is found by 
points on these sixteen radii, beginning at J by drawing a line at right angles to the radial 

AJ, then at right angles to the next radial on the left, and so on as shown by the position 

of the little trying-squares, the external angles of which designate points on which as centres 
with half the width of rail as radius describe arcs of circles. Touch ing these arcs trace 
the curved edges of the scroll; but at the point 0 where the arc touches the eye of the 
scroll measure on the radii from the external angles of the squares to tlie circle forming the 
eye, and set off these distances outward as at 0 0, S S, etc., to J, tracing the remainder of 
the convex curve from 0 to J through the points thus found. The spiral drawn in this way 
may be cut off at any point where a sufficient revolution is made. In this case it is cut off 
at D and connected with the plan at D, Fig. i. 

Fig. 5. Construction of Block for Scroll Step and Riser. 

Fig. 6. Scroll Step as Completed. 


I 

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P L A T e: 54 



























































































































PLATE 55. 

Hand-rail over Elliptic Staircase from the Plan given at Plate No. 7 , Fig. ii.—The best 

division of hand-rail for this plan is to begin at the centre, Fig. i, taking in this first piece a portion of rail including 
three treads each side of the minor axis; then Fig. 3 , covering four more treads. Fig. 5 . also taking four treads; and 
Fig. 8 , with the bottom tread and as much more of the curve as may be required to join the level rail at its usual 

height. After deciding on the proper number of pieces in which to divide the plan of hand-rail, draw the tangents ^or 

the whole as follows . Make B V tangent to the centre of rail at V , draw B N tangent to the centre line of rail at Y; 
draw N A tangent to the centre line of rail at W, draw A L tangent to the centre line of rail at C, the level tangent 
L F will be fixed further on. 

Fig. I, Plan of Wreath-piece including Six Treads.—Draw B X at right angles to B Y and equal to three 
rises; connect X Y , at right angles to B V draw V A equal to three ri.ses; join A B, prolong A V to F indefinitely, from 

Y through V draw YD; on B as centre with B A as radius describe the arc A D, parallel to B N draw M K, S R and W T; 

parallel to V A draw U 5, Q G and L J. 

To Find the Angle with which to Square the Wreath-piece at Both JointsProlong R S to F, par¬ 
allel to B V d raw G H; make V E equal H C; join E F. then the bevel at E contains the angle sought. 

Fig. 2 . Face-mould from Fig. i; also Showing the Squaring of the Wreath-piece at the Joints. 

— Let N A and N A each equal D N of Fig. i , make N B at right angles to N A and equal to N B of Fig. i ; join B A 
and B A ; make B J G 5 equal the same at Fig. i. Through J G 5 draw' K M, R S and T W parallel to N B ; make B P, 

J K and J IVI equal B P, L K and L M of Fig. 1 ; make G R, G S, 5 T and 5 W equal Q R, Q S, U T and U W of Fig. l. 

Apply the same measurements the other side of the centre B P, and through ail these points trace the curved edges 
of the face-mould. Make the joints A A at right angles to the tangents. This w'reath-piece is squared at both joints 
by the angle at bevel E of FiG. i. 

Fig. 3 . Plan of Wreath-piece including Four Treads.—Draw Y R at right angles to Y N and equal to four 

rises. Parallel to Y X draw N I; at right angles to A N draw W 5 and N, 14 ; make N, 14 equal 1 R ; join 14, W , draw W J 

parallel and equal to N Y ; make 1 S equal 14, N , parallel to Y N draw S G ; make G 8 parallel to 1 Y ; join 8 J parallel to 

8 J draw’ T M, 2, 9 N K. 7, 22 and 10, 11 , parallel to Y I draw O F and D 3 ; parallel to N, 14 draw' U P and C I ; at right 

angles to J 8 draw Y Z; on N as centre with N I as radius describe the arc 1 Z ; at right angles to J 8 draw W B , on N as 
centre w'ith W 14 as radius describe an arc at B ; join B Z. 

To Find the Angle with which to Square the Wreath-piece at the Joint over Y:—Draw 3 A parallel 
to NY, make Y E equal A 4; join E 2 : then the bevel at E contains the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over W Parallel to J 8 
prolong 7, 22 to 5, make W X equal U Q; join X 5; then the bevel at X contains the angle required. 

Fig. 5 . Face-mould from Plan Fig. 3 ; also Showing the Squaring of the Wreath-piece at the 

Joints. — Make Z L B equal Z L B of FiG. 3 : on B as centre with W, 14 of Fig. 3 as radius describe an arc at N; on L as 

centre with L N of Fig. 3 as radius intersect the arc at N ; join B N, N Z and L N; make B I P equal W I P of Fig. 3 ; 

make N 3 F equal N 3 F of Fig. 3 ; through I P, 3 F parallel to L N draw 11, 10, 7, 22, H S and T M ; make I 10, I 11, P 22, 

P 7, N 12, N K equal C 10, C 11, U 22, U 7, N 12, and N K of FiG. 3 ; make 3 9, 3 H, F M, F T equal D 9, D H, O M and O T of 

Fig. 3 . Through Z draw' T A; make Z A equal Z T, make the joints B and Z at right angles to the tangents; through 
A M, 9, 12, 22 and 10 of the convex and T H K 7, 11 of the concave trace the curved edges of the face-mould. The angle 

with w'hich to square the wreath-piece at joint is taken by bevel E, Fig. 3 , and for squaring joint B the bevel X of Fig. 3 . 

Fig. 5*—Make W T equal four rises. From A make A 6 parallel to W 14; make A B perpendicular to A C and equal 

to 6 T; join B C. This position of the plan with its tangents and angles of inclination is removed and completed at 

Fig. 6 . 

Fig. 6 . Plan of Wreath-piece over Four Treads, taken from Fig. 5 .—Make c N parallel and equal to 
A W ; make 6 J equal to A B ; make J H parallel to W A and H R parallel to W 6 , join R N and prolong to M indefinitely; 
prolong 6 W to IVI ; parallel to R N draw Z 4, K 3 and A X ; parallel to W 6 draw 2 F; parallel to A B draw O O , at right 

angles to N R draw W E and C D indefinitely: on A as centre with A 6 as radius describe the arc 6 E; again, on A as 

centre with B C as radius describe an arc at D ; join D E. 

To Find the Angle with which to Square the Wreath-piece at the Joint over wMake w L equal 
J G ; join L M ; then the bevel at L contains the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over cDraw cx 
at right angles to C A ; draw X Y at right angles to X C and equal to A V ; join Y C : then the bevel at Y contains the 
angle required. 

Fig. 7 . Face-mould from Plan Fig. 6 , Showing also the Squaring of the Wreath-piece at the 
Joints.—Make DUE equal D U E of Fig. 6 ; on D as centre with C B of Fig. 6 as radius describe an arc at A; on U as 
centre with U A of Fig. 6 as radius intersect the arc at A; join A E. A D and U A; make D O equal C Q of FiG. 6 ; 
make A H F equal A H F of Fig. 6 ; parallel to U A through Q draw’ Z 4; parallel to U A through H and F draw' P S 

and K 3 ; make Q Z, Q 4 and A T equal O 4, O Z and AT of FiG. 6 ; make H S, H P, F 3 and F K equal R S, R P, 2, 3 

and 2 K of Fig. 6 .; through D draw Z B; make D B equal D Z; through E draw K C; make E C equal E K; through 
B 4 A S 3 C of the convex and Z T P K of the concave trace the curved edges of the face-mould. The angle with 
which to square the w'reath-piece at joint D is taken by the bevel at Y; and for joint E by the bevel at L of Fig. 6 . 

Fig. 8 . Plan of Wreath-piece, including the First Tread.—To find the height CO set up an eleva¬ 
tion of the bottom step and tw’o rises as at Fig. 9 , let X be the centre of baluster and XO half the thickness of 
rail. Make HZ equal four inches and ZL half the thickness of rail; draw’ LC parallel to the floor-line; the angle 

at O must equal the angle B of FiG. 5 . Again at FiG. 8 make CO equal CO of FiG. 9 : from O parallel to C B 

draw O L; from L draw L F tangent to the centre line of rail at F; make F H at right angles to F L ; parallel to 

F L draw C G, U T and J R ; parallel to CO draw S P and R Q; at right angles to F L draw' C D, on L as centre 

W'ith L O as radius draw the arc O D; join D F. 

To Find the Angle with which to Square the Wreath-piece at the Joint over C:—Make C K 

equal C P; join K E : then the bevel at K contains the angle sought. 

To Find the Angle with which to Square the Wreath-piece at the Joint over FMake HG 

equal C O ; join G F : then the bevel at G contains the angle required. 

Fig. 10 . Face-mould from Fig. 8 , Showing also the Squaring of the Wreath-piece at the 
Joints.—Let F D equal F D of FiG 8 ; on F as centre w ith F L of FiG. 8 as radius describe an arc at L ; on D as centre 
with O L of Fig. 8 as radius intersect the arc at L; join F L and L D; make L X X equal L Q P of FiG. 8 ; through X X 

and D parallel to F L draw X J, T U and D N ; make L M, X T. X U and D N equal L M. S T, S U and C N of FiG. 8 . 

Make the joints at right angles to the tangents; make FS equal FJ; through D draw QP; make DP equal DU; 
through S Nl Q U of the convex and J T N P of the concave trace the curved edges of the face-mould. This face- 

mould will not answer for the top of the flight, because at the top, although including but one tread as at the bottom 

and setting up the usual height from the floor for the level rail, yet the total height is greater. This will be under¬ 
stood by examining Fig. ii— which is set up for the top—and comparing it with Fig. 9 . 


Plate No. 55 

























































PLATE 



Figs. I and 2. Wreath-piece from a Face mould, with Tangents at Right Angles, the Position 
of one of which Tangents B L is Inclined, while that of L D is Horizontal.— The sliding of the face- 
mould along the joint C D and at F, tlie other side of the stuff, to plumb the sides of the wreath-piece, 
is shown by the dotted lines. The sides G H, J K of the wreath-piece at the centre butt-joint are not 
straight lines. On the concave side of the wreath-piece G H is a concave curve, and J K of the convex a 
convex curve on that side. This is true also of all wreaih-pieces having butt-joints falling within a cir¬ 
cular plan, but these straight sides are corrected in the hands of a skilful rail-worker, who, leaving some 
over-wood—after the two pieces are bolted together—works the sides plumb with the proper-shaped tools 
Fig. 2 shows the wreath-piece with the concave side cut away plumb. When this side is worked plumb, 
a gauge, like Fig. 8 , having an arm provided with a large pencil, may be used to mark the width on 
the convex side; next the top is shaped, and from this the thickness is gauged. The directions here 
given with regard to this wreath-piece apply generally to all, but particularly to the following; 

Plate 24, Fig. 3, Plate 25, Fig. 6, Plate 26, Fig. 6, Plate 27, Fig. 6, 

“ 32. “ 3. ‘‘ 37 . “ 4 . “ 40. “ “ 43. “ 3 . 

“ 44. “ 5 . “ 46. “3. “ 54. “ 3 - 

Figs. 3 and 4. Squaring a Wreath-piece from a Face-mould, both Tangents of which are 
Inclined either on a Common Inclination or on Different Inclinations. —The angle with which to square 
a wreath-piece at the butt-joint is the inclination of the face of the plank along the joint given by the 
face-mould, in connection with a line on the joint—which is square through the plank—that coincides 
with a vertical plane; hence it is commonly understood as an angle giving a plumb-line on a butt-joint 
To Determine tlae Direction in which to Apply the Angles for Squaring a Wreath-piece at the 
Joints :—Place the lower end of the wreath-piece towards you, turn the upper end to the right or left 
to suit the hand of the stairs, then move the face-mould up a few inches on the slide-line as at Fig. 3 , 

and it will be seen that as the centre of the joint J is carried toward K, the plumb-line must apply in 

the direction K M passing through the centre L, and at the upper end the othei’ tangent will be moved 
towards N, showing that the plumb-line on that joint must lie in the direction N P, passing through the 
centre 0. 2'he pla7ik edge A D, bevels U and V, slimv at otice the correct position of bevels. 

Another Way of Deciding the Direction in which to Apply Plumb-lines on Butt-joints is as 

Follows: —Holding the wreath-piece as before directed, cant it up on the corner F—a position it must 
take—when it will be at once evident that the plumb-line must apply in the direction K M. This causes 
the stock of the bevel to lay towards the cpnvex ; then at the upper joint reverse the stock of the 

bevel, placing it towards the concave as shown ; also the slide-line need not be used, but the tangent 

line K J (squared from the joint at K) and the face-mould tangent moved on this line until it reaches 

the point S and N of the upper end. 

To Put the Face-mould in Position on the Planes of the Plank so that its Edges will Mark 
the Plumb Sides of the W^reath-piece :—Hold the wreath-piece as before explained ; square a line from 

the joint at K, K J indefinitely ; slide the face-mould up from the lower end along the slide-line until 

J—the centre of the face-mould joint—falls on the line K J, K being a point at the face of the plank 

of the previously-applied plumb bevel K M ; then again when the face-mould is in this position its tan¬ 

gent at the upper end will touch the point N of the pIuiTib-line N P on the upper joint ; also the con¬ 
cave edge of the face-mould will touch S of the plumb-line S T. Apply the face-mould to the other side of 
the wreath-piece on the slide-line, keeping the joint J of the face-mould as much below the joint of the 
wreath-piece as it is above it on this side. 

Fig. 4. The Wreath-piece Shown with the Concave Side Cut Away Plumb.— In all face-moulds 
of this character, where a level line passes through the centre from which the plan of the rail is described 
—the minor axis—there is a place where the plane of the plank is level, and this point on the width X Y 
and through the thickness X T is the normal place in a wreath-piece, and where the over-wood is removed 
equally parallel to the faces of the plank. In shaping the wreath-piece the centre line of the thickness of 
rail will correctly touch R and U, the centre at the joints, and S the centre of the plank. When the face- 
mould is in position to plumb the sides of the wreath-piece, if the normal place is marked at V and W, the 
plumb-line V W will pass through the centre of stuff at S, and give the direction in which to move the 
round-faced plane in working the sides of the wreath-piece plumb. In ganging the wreath-piece to a width, 
the long arm of the gauge should be held in the direction of the plumb-line W V. The instruction gn>en under 
the head of Figs. 3 and 4 apply particularly to the follounng : 


Plate 25, Fig. 4, 

‘ ‘ 31, “ 2 and 4, 

“ 40. “ 3. 

“ 46, “ 5. 

” 53. “ 6, 


Plate 26, Fig. 6, 

“ 36. " 3. 

“ 41. “ 4. 

“ 47. “ 4. 


Plate 27, Fig. 4, 

“ 37, “ 7. 

“42, “ 4 and 6, 

“ 50, “ 6, 


55. 


2, 4 and 7. 


Plate 28, Fig. 4, 

“ 38, “ 4. 

“ 43. “ 5. 

“ 51. “ 3 and 5. 


Plate 29. Fig. 4, 

“ 39. “ 4. 

“ 44. “ 4. 

“ 52. “ 4. 


Fig. 5. Wreath-piece from a Face-mould over a Plan of Less than a Quarter-circle, the 
Position of A K, one of the Tangents, being Level, the other, K Z, Inclined.— The dotted lines show 
the face-mould as placed at the joint D to plumb the sides of the wreath;* the tangent A of the face-mould 
is brought to C on the other side of the wreath-piece. The sliding of face-moulds of this character is always 
along the joint, which is at right angles to the level tangent, the same as Fig. i. The above instructions 
apply particularly to the following; 


Plate 24, Fig. 6, 'Plate 30, Fig. 2 and 4, Plate 32, Fig. 6, Plate 33, Fig. 3, Plate 48, Fig. 4, 

“ 49. “ 3. “ 50, “ 5 and 7, “ 53, “ 5 and 7, “ 55, “ 10. 

Figs. 6 and 7. How to Determine the Least Thickness and Width of Wood Required for any 

Wreath-piece of any Form of Rail. —From the centre of the thickness and width of the proposed form 
of rail describe a circle enclosing the form ; then the diameter of such a circle will be both the least 

thickness of the plank, and also the least width of the wreath-piece out of which the twist can be 

worked. 


* At Fig. 5 and the list given in the application of the angles to square ivreath-pieces at the joints, the stock of the bevel at 
both joints lies towards the convex side of the wreath-piece as show)i. 






P L AX E N o. 5 6 . 


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F I G 3 



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F I G. 4 . 







F I G. 7. 
















































































PLATE 57. 

• 

Fig. I. Plan of Stairs Suitable for Wholesale Stores. —These stairs from the first to 
the second story are enclosed with panel-work as shown by the elevation Fig. 4 . The door 
to shut off communication between the two stories is often placed on the platform, and in 
that case the platform is so situated that the door trims under the end of the well-hole. 
Side-rails are hung on strong ornamental iron brackets, sometimes on both sides of wide flights. 
The newel-posts are never less than seven inches, and those at the top of the flights are 

continued below the ceiling, finishing at the lower end with turned work. 

Fig. 2. Construction of Close String Paneled. —This finish of string is used in the 

upper flights that are furnished with hand-rail and balusters, as at Fig 5 The well-holes of 

each story are framed shorter than the run of the flights above, so that each flight starts 
from the floor below\ resting directly on the floor-beams. 

Fig 3 . Panel-work. —By this plan the middle muntins A are wider than the face-muntins 
D. so that the mouldings may be nailed free from the panels, allowing the latter to shrink 
without disturbing the mouldings. 



Fig. 


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1?LATE 5 8. 

Fig. I. Plan of the Landing Portion of a Staircase with Square Corner-pieces 

like Small Low-down Newels set in the Angles with a Continued Hand-rail Over.— 

This plan is given at Plate No. 6 , Fig. 6 L and M are 3 ^" square angle-pieces that are 

brought above the platform and floor as shown in’ connection with the elevations Figs 3 and 

. 4 . The centres of balusters A and B are equal in distance to A and Q. The square angle 

at the corner-piece L is turned for the continued hand-rail one quarter C D V, C R S, using 

only radius from the face of the corner-piece E to D, then from the joint D R of the level 

quarter another is taken at the ramp to ease over to this level, as shown at the elevation 
Fig 3 , Z X and X K. 

Fig. 2. Design and Construction of Close Front-string. —The drawing to the scale 
given will be a sufficient explanation 

Figs. 3 and 4. Elevation of Treads and Rises, including the Square Corner-piece 
Connecting with the Platform, the String and the Level as given at Plan Fig. i.— 

0 P equals 0 P of Fig. i. The face P E of the corner-piece L. Fig. i, is along the line PEZ; 

Z X equals D E of Fig. i; Z K equals one inch; the joint J H connects with D R of Fig i 

The height to the bottom of rail Y from the step at the line of rise W is 2 '.i". The height 

from floor to bottom of level rail S J is 2 '. 6 ". C D, V V is the carriage-timber, showing its 

bearing against the front platform-timber at V V. F, N and T are places of mortices to receive 
the tenons of string. The baluster at B is intended to be set three eighths of an inch into 
the mill-plowed hand-rail, as shown at the section A, and then pieces set between each baluster, 
thick, thus leaving a finished panel or sinkage of the depth of which gives a much better 
appearance to the bottom of the rail than when flush. 



P LAT E No. 58. 



Scale 1 V2 in.= 1 ft. 












































































































































































































































































PLATE 59. 

Fig. I. Plan of the Upper Portion of a Quarter Platform Staircase with Square- 
moulded Newels set in the Angles.— This plan is given at Plate No. 7 , Fig. 5 . The dotted 
lines show a portion of the rough framing of the platform. 

Fig. 2. Design Elevation and Details of Plan Fig. i. —Through this elevation the 

lengths of the angle newels and the connections of hand-rail, balustrade work, strings, etc., are 
obtained. The face of the newel marked A at the lower end showing its connections is face A at 
plan Fig. i ; also the face of the newel marked E at the lower end is face E at plan Fig. i. 

Fig. 3. Laying Out the Newel connected with the Platform, the Sides of which are 
Lettered on the Plan Fig. I, A B C D.—The four faces of this newel are lettered at tiie top to 
correspond with the plan Fig. i. J K is the total length of the newel-shaft as taken from J K 

of the elevation Fig. 2 . The distances marked by the letters J L M N indicate principal points 

of measurement taken from the corresponding letters of the A side of newel. Fig. 2 ; and the 
same may be said of the letters 0 P Q at face D ; the sides B and C will be understood by 
comparing them with their adjoining sides and connections, and B and C of Fig. i. 

Fig. 4. Laying out the Landing Newel the Sides of which are Lettered on the 
Plan Fig. I, E F G H.—The letters at the top of these sides correspond with those of the plan 
Fig. I. R S of the side E marks the total length of this newel-shaft, and T U V the prin¬ 
cipal points of measurement lettered the same at Fig. 2 . W X Y of the connection at the 

side F are also the principal points of measurement taken from the elevation of the landing 

newel. Fig. 2 . The sides H and G will be understood by examining them in connection with 

the adjoining sides and G and H of Fig. i. 

Fig. 5. Balustrade Moulding as Shown in Place at the Elevation Fig. 2. 

Fig. 6. Construction of Square Newel-posts. —The narrow pieces forming the sides A 
and B of the newel-shaft should have blocks glued to the inside faces at the edges—not 

more than one foot apart—when the glue is set to be jointed with the edges square from 

the face ; also to guard against the joints giving way, hard-wood dowels ought to be set 
in as shown at suitable intervals. The sides of the newel-shaft would he better if put together 
with good mitre-joints blocked and do7velled as before. 



E No. 5 9. 



/ 




































































































































































































































































































































































































PLATE 6 0. 

Plan and Side Elevation of a Quarter-turn Open Newel Platform Stairs. —Design 
and construction for moulded close front-string, turned newel and balusters; the hand-rail with 
ramp and knee. 


( 










F 





























































































































































































































































PLATE 61. 

Design for Newels, Turned Balusters, and Close Front-string. 




f 


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L 

















































































































































































PLATE 62. 

Plan ot Stairs Turning One Quarter, with Platform and Two Risers Curved at 
their Front Ends to Newel. —The plan is designed to dispense with winders and give a 
comfortable, easy stairs for travel, taking but a few inches more room than the usual winders 
that are required to make a quarter-turn. The small newel receives the straight rail of the 
flight and the level hand-rail at the landing, as shown by the side elevation. This arrange¬ 
ment requires no twists or easements; the only turn of the hand-rail is the level quarter. 
See Plate 5. Fk;. 7. 



Plate No. 62. 





































































































































PLATE 63. 

Design for Angle Newel and Turned Baluster, with Square Base and Top; also 
Design and Construction of Close Front-string Paneled and Moulded. 



/ 
































































































































































































PLATE 64. 

Design for Open Moulded Front-string and Balusters.—The balusters to be bolted 
the face of the string. 








f i 






































































































































PLATE 65. 

Design for Angle Newel, and Turned Ealusters with Square Tops and Bases; 
also Design and Construction of Close Front-string Paneled and Moulded. 










P L AT E N 0. 65 . 











































































































































































































PLATE 66. 

Fig. I. Design for a Turned and Carved Newel, Carved String and Balustrade. 

Fig. 2. Design for Spiral, Turned Newels and Balusters; Bracketed String; Hand¬ 
rail with Ramp and Goose-neck. 

Figs. 3 and 4. —The bottom riser of the upper flight is set one tread from the centre 
of newel, as shown on the plan Fig. 3, and the elevation Fig. 4. If, on the contrary, the 
bottom riser referred to should be placed at the centre of the newel it would then be necessary 
to make that newel one rise higher from the platform to receive the hand-rail of the upper 
flight. This difference in the heights of the two newels from the same platform is objected 
to by some, hence these sketches and explanations. 









Plate No. 66,^ 

































































































































































































PLATE 67. 

Ancient Staircase at Rouen, France. — From the Moniteur des Architectes. 
Architect and Building News." 


“ A77ierican 



Plate No. 67 



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frpatme AonueuR. 

DE5 AR-CHITECTE5^ 









































































































































PLATE 68. 

Interior View of a Flight of Stairs Turning One Quarter, with a 
Starting Two Rises Up; the Platform Ornamentally Enclosed on 
Fancy Panel-work to Match the Hall Wainscot; and Above which 
Hall, Spindle Screen Panels between Columns. 


Platform at the 
One Side with 
and Across the 




.Plate No. 68. 















































































































































































































































































































































































































































































PLATE 69. 

Interior View of a Grand Staircase, and Spacious, Elegantly Fitted Hall. 








PlXte No. 69. 









































































































































































































































































































































































































































































































PLATE 70. 


Designs for Newels. 



Plate No. 70. 



Scale It lN.= irT. 




















































































































































































































































































































































































































PLATE 71. 


Designs for Newels. 





Plate No. 71. 





































































































































































































































































































PLATE 72. 


Designs for Newels. 




r 


Plate No. 72. 































































































































































































PLATE T3. 


Sections of Hand-rails of Various Forms and Full Size. 





















Sections of Hand-rails of Various Forms and Full Size. 

































PLATE 75. 


Newels and Balusters. 
























































































































































































































































































































































































































































































































PLATE 76. 


Newels and Balusters. 



Plate No. 76. 


I 



Newels and Balusters of these designs are manufactured by the Standard Wood-Turning Co., 200 Greene St., Jersey City, N.J. U.S.A 



































































































































































































































































































PLATE 77. 


Newels and Balusters. 



Plate No. 77 
















































































































































































































PLATE 78. 

The Tangentograph. 


Plate 78. 

THE TANGENTOGRAPH. the following figs, represent the use of the instrument. 





Fig. 4. 

Shows the application 
of the bevels. 


Shows the instrument as applied for marking: 

moulds; also i^ivinjr bevels f('r 


tangents for face- 
the joints. 


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MONCKTON’S 

Practical Geometry 

BEING A 

SERIES OF LESSONS BEGINNING WITH THE SIMPLEST PROBLEMS AND 
IN THE COURSE EMBRACING ALL OF GEOMETRY LIKELY TO BE 
REQUIRED FOR THE USE OF EVERY CLASS OF MECHANICS 
OR THAT ARE NEEDED FOR INSTRUCTION 
IN MECHANICAL SCHOOLS. 

ILLUSTRATED BY 42 FULL PAGE PLATES. 


BY 

JAMES H. MONCKTON, 

Author of Monckton’s “National Carpenter and Joiner,” and Monckton’s “ National Stair Builder.” 
Instructor for many years of the Mechanical Class in “ The General Society of Mechanics 
and Tradesmen’s Free Drawing School ” of the City of New York. 


CO N TENTS. 


I.VTRonvCTiov. Drawing instruments, tools and materials required to be¬ 
gin witli, and now to use them. A I' square. Right angle tnangles. 
Drawing boards and lacks. The compasses and its a lachments. The 
line pen. Proper way to handle compasses. The lead pencil. Six 
rules for using the drawing instruments. 

Plate i. Geometry. A point. A line. A curve line. A composite line. 
A mixed curve. A zigzag line. A vertical line. A level line. A per 
peiidicular. 

Pl.ate 2. A circle. The radius. The diameter. A segment of a circle. 
Concentric circles. Eccentric circles. A tangent. T.ngent circles. 

Plate 2. To erect a perpendicular from a given line. Parallel lines. 
Oblique lines. An angle. Curvilinear angles. Mixtilinear .angles. 
To bisect a line. 

Plate 4. To bisect an angle. A diagonal. To erect a perpendicular at 
the end of a given line. To let fall a perpendicular to a given line 
from a given point. Angles. To trisect a quarter circle. To inscribe 
a square in a circle. 

Plate 5. A superficies. A plane figure. An equilateral triangle. An 
isosceles. A scalene and a right angled triangle. A square. An 
oblong A rhombus. A rhomboid. A trapezoid. A trapezium. Quad¬ 
rilaterals and tetragons. 

Plate 6. Polygons and their construction. From a given side to con¬ 
struct an equilateral triangle, a square, a pentagon, and a hexagon. 

Plate 7. To inscribe an octagon within a square (two methods). Alti¬ 
tude or height of a triangle. An angle nscribed in a semicircle. To 
inscribe a square within a square. An equilateral triangle inscribed in 
a circle. To circumscribe a square about a circle. 

Plate 8. To place a line at right angles to a given line by the use of any 
sca'e of equal pans, and its application for a mechanical purpose. To 
circumscrioe an equilateral triangle about a given circle. To find the 
centre of a circle. To inscribe a circle in a triangle. 

Plate 9. To copy an angle. To copy an irregular angular figure. To 
describe a circle through any three points not in a straight line. To 
find a right line equal to the semicircumference of a circle. 

Plate 10. To find the circumference of a circle bv another method. Con¬ 
vex and concave. The square of the hypoihenuse of a right angled 
triangle is equal to the sum of the other two sides. 

Plate ii. To construct a triangle from given sides. To divide a circle 
into six equal p.irts; into eight equal parts; into twelve equal parts. 

Plate 12. Measurement of angles. Rapid method of dividing a given 
space into any number of equal parts. 

Plate 13. To divide a line into any number of equal parts. 

Plate 14. Measure of the angle at the centre and circumference of the 
circle. To make a square equal to three given squares. To describe an 
ellipse (two methods). 

Plate 15. Three methods of describing the ellipse. 

Plate 16. Two other methods of describing the ellipse. To draw a tan¬ 
gent to a given point on the ellipse. To find the point of contact. 


Plats 17. To find the axis of a given ellipse. To circumscribe a rectan¬ 
gle by an ellipse. To rind the axis of an ellipse proportioiiul to the axis 
of a given ellipse. Parallel elliptic lines impossible. To d.scribe an 
approximate ellipse with arcs of circles. 

Plate 18. To describe an approximate ellipse more accurately. To de¬ 
scribe an eggoiJ. To describe a simple spiral or stroll with arcs of 
circles. 

Plate 19. To describe an egg-shaped oval with arcs of circles. To de¬ 
scribe a cycloid. To destiibe an epicycloid. 

Plate 20. To describe an epicycloid by a circle rolling within another cir¬ 
cle. To describe an involute. To describe a spiral or involute of one 
or more revolutions. 

Plate 21. Arches. A semicircular arch. A platband. The elliptic arch. 

Plate 22. To describe various forms of gothic arches. 

Plate 23. A rectangular prism. The cube. A cube cut by a plane pass¬ 
ing through the diagonals. Cut by a plane through the cenlie. 

Plate 24. A square prism cut at any height. To develop the surface of 
the truncated prism. 

Plate 25. A pyramid. A triangular prism. A hexagonal prism. A square 
pyramid. A hexagonal pyramid. 

Plate 26. A regular tetrahedron. A regular octahedron. The dodecahe- 
dion. The icosahedron. 

Plate 27. A right cylinder. To find a section. To find an envelope. 

Plate 28. To find the section of a right cylinder cut obliquely. To find 
the envelope. 

Plate 29. A cylindroid To find the section. 

Plate 30. To find the section of a cylindroid cut obliquely in two direc¬ 
tions. A sphere. The covering of a sphere. 

Plate 3r. To describe the covering of t sphere on lines parallel to centre 
plane. The sections of a sphere. Prolate spheroid. Sections of a pro¬ 
rate spheroid 

Plate 32. Covering of a prolate spheroid. An oblate spheroid. Sections 
of an oblate spheroid Covering of an oblate spheroid. 

Plate 33. The helix. 

Plate 34. The cone and its sections. 

Plate 35. The ellipse tiom a cone. The parabola. The hyperbola. 

Plate 36. To describe the parabola by another method. The ellipse from 
a cone. 

Plate 37 To describe a parabola by the intersection of tangent lines. 
The iivperbola on the principle that seciions of a cone parallel to the 
base are circles. To develop the covering of a cone. 

Plate 38 To develop the covering of a cone, with the tmee of the inter¬ 
section, when an hyperbola—also when a parabola—is produced by 
cutting plane. 

Plate 39. To develop the covering of an oblique cone together with the 
traces of several cutting planes. 

Plate 40. Scale of equal parts. A diagonal decimal scale. 

Plate 41. The protractor. The straight protractor. 


WILLIAM T. COMSTOCK, Publisher, 23 Warren St., New York. 











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